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EExamplebook
SSC CombinedGraduate Level-Tier-
I,II
2013
Shiv
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SSC UPSC previous years solved questions with answers
Arithmetical Ability
1. The product of 2 numbers is 1575 and their quotient is 9/7. Then thesum of the numbers is
a. 74
b. 78
c. 80
d. 90
Ans : Let the numbers be x and y .
xy = 1575
And x/y = 9/7
xy/x/y = 1575/9/7
y2 = 1225
y = 35 and x = 45
The sum of the numbers = 45+35
= 80
2. The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is __
a. 3
b. 6
c. 9
d. 8.2
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Ans : (81)3.6 * (9)2.7/(81)4.2 * (3) = (3)14.4 * (3)5.4/(3)16.8 * (3)
= 314.4+5.4-16.8-1
= 32
= 9
3. 6+6+6+ is equal to
a. 2
b. 5
c. 4
d. 3
Ans : Let 6+6+6+. be x.
x =6+x
x2 = 6+x
x2 + x 6 = 0
(x-3) (x+2) = 0
x = 3
4. The sum of the squares of two natural consecutive odd numbers is 394.The sum of the numbers is
a. 24
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b. 32
c. 40
d. 28
Ans : Let the consecutive odd numbers be x and (x+2)
x2 + (x + 2)2 = 394
x2 + x2 + 4x + 4 = 394
2 x2 +4x 390 = 0
x2 + 2x 195 = 0
(x +15) (x-13) = 0
x = 13
Required sum = 13 +15 =28
5. When (6767 +67) is divided by 68, the remainder is-
a. 1
b. 63
c. 66
d. 67
Ans: (6767+ 67) = 67(6766 + 166)
As 66 is an even number
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6766 is an even number
(6766 + 1) is perfectly divisible by (67 + 1)
i.e. 68
The remainder = 67
6. In a division sum, the divisor is 4 times the quotient and twice theremainder. If a and b are respectively the divisor and the dividend then-
a. 4b-a2 /a =3
b. 4b-2a /a2 =2
c. (a+1)2 = 4b
d. A(a+2)/b = 4
Ans : As divisor is a, and dividend is b.
Quotient = a/4
And Remainder = a/2
b = a * a/4 + a/2
4b = a2 + 2a
a(a+2)/b = 4
7. If 738 A6A is divisible by 11, then the value of A is-
a. 6
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b. 3
c. 9
d. 1
Ans : As 738A6 A is divisible by 11.
A + A + 3 = 6 + 8 + 7
A = 9
8. The east positive integer that should be subtracted from 3011 * 3012 sothat the difference is perfect square is-
a. 3009
b. 3010
c. 3011
d. 3012
Ans : 3011 * 3012 = 3011 (3011 + 1)
= (3011)2 + 3011
Required least number = 3011
9. P, Q, R are employed to do a work for Rs. 5750. P and Q together
finished 19/23 of work and Q and R together finished 8/23 of work. Wage of
Q, in rupees, is-
a. 2850
b. 3750
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c. 2750
d. 1000
Ans : Work done by Q = 19/23 + 8/23 1
4/23
Wage of Q = 4/23 * 5750
= Rs. 1000
10. A can do a piece of work in 24 day, B in 32 days and C in 64 days. Allbegin to do it together, but A leaves after 6 days and B leaves 6 days before
the completion of the work. How many days did the work last?
a. 15
b. 20
c. 18
d. 30
Ans : Work done by A = 6/24 =
Work done by B = (x-6)/32
(where x is no. of days in which work is competed)
+ x 6/32 + x/64 = 1
16 + 24 12 + x /64 = 1
3x + 4 = 64
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x = 60/3 = 20 days
11. The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-
a. 1
b. 2
c. 3
d. 4
Ans : The square root of
[(0.75)3/1 0.75 + {0.75 + (0.75)2 + 1}]
= 1.6875 + 2.3125
=4
= 2
12. Given that 4096 = 64, the value of 4096 + 40.96 +0.004096 is-
a. 70.4
b. 70.464
c. 71.104
d. 71.4
Ans : Given Exp. = 4096 + 40.96 +0.004096
= 64 + 6.4 + 0.064
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= 70.464
13. By selling an article at 3/4th of the marked price, there is a gain of
25%. The ratio of the marked price and the cost price is-
a. 5 : 3
b. 3 : 5
c. 3 : 4
d. 4 : 3
Ans : Let of M.P. be Rs. x.
S.P. = Rs.3x/4
and C.P. = 3x/4 * 100/125
= Rs.3x/5
required ratio = x: 3x/5
= 5:3
14. A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in
the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, themonthly income of B is-
a. Rs.7,000
b. Rs.14,000
c. Rs.5,000
d. Rs.10,000
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Ans : Let the monthly income of B be Rs. x.
Monthly income of A = Rs. 2x and
Saving of A =5000 * 4/(4 + 1)
= Rs. 4000
Saving of B = Rs.1000
2x 4000/x-1000 = 5/3
6x 12000 = 5x 5000
x = Rs.7000
15. The ratio of the sum of two numbers and their difference is 5:1. Theratio of the greater number to the smaller number is-
a. 2 : 3
b. 3 : 2
c. 5 : 1
d. 1 : 5
Ans : Let the numbers be x and y.
x + y/ x y = 5/1
5x 5y = x + y
4x = 6y
x/y = 6/4
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x : y = 3 : 2
16. A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours
respectively, and C can empty it in 1 hour. If the pipes are opened at 3p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be
empty at-
a. 7.12 p.m.
b. 7.15 p.m.
c. 7.10 p.m.
d. 7.18 p.m.
Ans : Let the cistern be emptied at x p.m.
x -3/3 + x 4/4 = x - 5/1
4x 12 + 3x 12/12 = x 5/1
7x 24 = 12x 60
5x = 36
x = 36/5
= 7 hr. + 12 min.
= 7.12 p.m.
17. If A works alone, he would take 4 days more to complete the job than if
both A and B worked together. If B worked alone, he would take 16 daysmore to complete the job than if A and B work together. How many days
would they take to complete the work if both of them worked together?
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a. 10 days
b. 12 days
c. 6 days
d. 8 days
Let x days are taken when they work together.
Time taken by A to complete the work = (x + 4) days
And Time taken by B to complete the work = (x + 16) days
1/x = 1/x + 4 + 1/x + 16
1/x = x + 16 + x + 4/(x + 4) (x +16)
2x2 + 20x = x2 + 20x +64
x2 = 64 (8)2
x = 8 days
18. 250 men can finish a work in 20 days working 5 hours a day. To finish
the work within 10 days working 8 hours a day, the minimum number ofmen required is-
a. 310
b. 300
c. 313
d. 312
Ans : Required no. of men = 250 * 5 * 20/8 * 10
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c. 16 2/3%
d. 16 1/3%
Ans : Let the M.P. be Rs.100.
S.P = (100-40) = Rs.60
and C. P. = 60 * 100/(100-30) = Rs.600/7
Reqd. % profit = 100-600/7 /600/7 * 100%
= (700 600)/7 * 600 * 100 * 7%
= 16 2/3%
21. Successive discount of 10% , 20% and 50% will be equivalent to a
single discount of-
a. 36%
b. 64%
c. 80%
d. 56%
Ans : Equivalent to a single discount
= [100 - (100 10) (100 20) (100 50)/100*100]%
= [100 - 90*80*50/10000]%
= [100-36]%
= 64%
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22. A retailer offers the following discount schemes for buyers on an article-
I. Two successive discounts of 10%
II. A discount of 12% followed by a discount of 8%.
III. Successive discounts of 15% and 5%
IV. A discount of 20%
The selling price will be minimum under the scheme-
a. I
b. II
c. III
d. IV
Ans : From (i) single discount = [10 + 10 10*10/100] % = 19%
From (ii) single discount = [12 + 8 -12*8/100] % = 19.04%
From (iii) single discount = [15 + 5 15*5/100] % = 19.25%
From (iv) single discount = 20%
The S.P. will be minimum under the scheme IV.
23. Of three numbers, the second is thrice the first and the third number is
three-fourth of the first. If the average of the three numbers is 114, thelargest number is
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a. 72
b. 216
c. 354
d. 726
Ans : Let the first number be x.
Second number = 3x and Third number = 3x/4
x + 3x + 3x/4 = 3*114
19x/4 = 342
x = 342*4/19 = 72
The largest number = 3*72
= 216
24. A car covers 1/5 of the distance from A to B at the speed of 8 km/hour,
1/10 of the distance at 25 km per hour and the remaining at the speed of 20km per hour. Find the average speed of the whole journey-
a. 12.625 km/hr
b. 13.625 km/hr
c. 14.625 km/hr
d. 15.625 km/hr
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Ans : If the whole journey be x km. The total time taken
= (x/5/8 + x/10/25 + 7x/10/20) hrs
= (x/40 + x/250 + 7x/200) hrs
= 25x + 4x + 35x/1000
= 64x/1000 hrs
Average speed = x/64x/1000
= 15.625 km/hr
25. The average of 3 numbers is 154. The first number is twice the second
and the second number is twice the third. The first number is-
a. 264
b. 132
c. 88
d. 66
Ans : Let the first number be x.
Second number = x/2 and Third number = x/4
x + x/2 + x/4 = 3 x 154
7x/4 = 462
x = 462*4/7
=264
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26. The average salary of all the staff in an office of a corporate house is
Rs. 5,000. The average salary of the officers is Rs. 14,000 and that of therest is Rs. 4,000. If the total number of staff is 500, the number of officers is
a. 10
b. 15
c. 25
d. 50
Ans : Let the number of officers be x.
5000*500 = 14000x + 4000(500-x)
2500000 =14000x + 2000000 4000x
x = 500000/10000
= 50
27. The average marks of 40 students in an English exam are 72. Later it is
found that three marks 64, 62 and 84 were wrongly entered as 60, 65 and73. The average after mistakes were rectified is-
a. 70
b. 72
c. 71.9
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d. 72.1
Ans : Correct average
= 40*72 + (64 + 62 +84) 68 65 73/40
= 2880 + 210 206/40 = 2884/40
= 72.1
28. A and B are two alloys of gold and copper prepared by mixing metals in
the ratio 7:2 and 7:11 respectively. If equal quantities of the alloys are
melted to form a third alloy C, the ratio of gold and copper in C will be-
a. 5 : 7
b. 5 : 9
c. 7 : 5
d. 9 : 5
Ans : Quantity of gold in A = 7/9* wt. of A
Quantity of gold in B = 7/18* wt. of B
If 1 kg of each A and B are mixed to form third alloys C.
Then quantity of gold in 2 kg C = 7/9 + 7/18
= 7/6 kg
And Quantity of copper in 2 kg C = 2 7/6
= 5/6 kg
Required ratio = 7/6 : 5/6 = 7 : 5
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29. In a laboratory, two bottles contain mixture of acid and water in theratio 2 : 5 in the first bottle and 7 : 3 in the second. The ratio in which thecontents of these two bottles be mixed such that the new mixture has acid
and water in the ratio 2 : 3 is-
a. 4 : 15
b. 9 : 8
c. 21 : 8
d. 1 : 2
Ans : Quantity of acid in first bottle = 2/7 x mix.
and Quantity of acid in second bottle = 7/10 x mix.
If x and 1 volumes are taken from I and II bottle respectively to form new
mixture.
Then, (2/7 x + 7/10 * 1)/(5x/7 +3/10 * 1) = 2/3
6x/7 21/10 = 10x/7 +6/10
4x/7 = 15/10
x = 15/10*7/4 = 21/8
Required ratio = x : 1
= 21 : 8
30. A mixture contains 80% acid and rest water. Part of the mixture thatshould be removed and replaced by same amount of water to make the ratio
of acid and water 4 : 3 is-
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a. 1/3 rd
b. 3/7 th
c. 2/3 rd
d. 2/7 th
Ans : Let the initial wt. of mixture be 1 kg and x kg of mixture is taken out
and replaced by same amount of water.
Amt. of acid/Amt. of water = 0.8 0.8x/ (0.2 0.2x + x) = 4/3
2.4 2.4x = 0.8 + 3.2x
5.6x = 1.6
x = 1.6/5.6 = 2/7th part
31. An employer reduces the number of his employees in the ratio 9 : 8 and
increases their wages in the ratio 14 : 15. If the original wage bill was Rs.
189,900, find the ratio in which the wage bill is decreased-
a. 20 : 21
b. 21 : 20
c. 20 : 19
d. 19 : 21
Ans : Let the initial number of employees be 9x and the employer gives Rs.
14y as wage to each.
9x * 14y =18900
xy = 150 and The later bill = 8x*15y = 120xy
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= 120*150 = 18000
Required ratio = 18000 : 18900
= 20 : 21
32. The batting average for 40 innings of a cricketer is 50 runs. His highest
score exceeds his lowest score by 172 runs. If these two innings areexcluded, the average of the remaining 38 innings is 48 runs. The highestscore of the player is-
a. 165
b. 170
c. 172
d. 174
Ans : Let the max. number of runs be x.
The lowest score = (x-172)
40*50 = 38*48 + x + (x-172)
2000 = 1824 + 2x 172
x= 174
33. Walking at 3 km per hour, Pintu reaches his school 5 minutes late. If hewalks at 4 km per hour he will be 5 minutes early. The distance of Pintusschool from his house is-
a. 1 Km
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b. 2 Km
c. 2 Km
d. 5 Km
Ans : Distance of the school from the house
= 4*3/(4 3) * 5 +5/60 km
= 12*1/6
=2 km
34. Nitin bought some oranges at Rs. 40 a dozen and an equal number atRs.30 a dozen. He sold them at Rs. 45 a dozen and made a profit of Rs.480.
The number of oranges, he bought, was-
a. 48 dozen
b. 60 dozen
c. 72 dozen
d. 84 dozen
Ans : Let the number of oranges bought be x.
45x/12 70x/24 = 480
(45-35)/12 = 480
x = 480*12/10 = 576
= 48*12 = 48 dozen
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35. A man buys two chairs for a total cost of Rs.900. By selling one for 4/5
of its cost and the other for 5/4 of its cost, he makes a profit of Rs.90 on thewhole transaction. The cost of the lower priced chair is-
a. Rs.360
b. Rs.400
c. Rs.420
d. Rs.300
Ans : Let the cost price of 1 chair be Rs. x.
C.P. of other chair = Rs. (900-x)
4/5 x + 5/4 (900-x) = 900 + 90
4/5 x +1125 -5x/4 = 990
9x/20 = 135
x = 135*20/9
= Rs. 300
C.P. of the lower priced chair is Rs. 300.
36. By selling 100 oranges, a vendor gains the selling price of 20 oranges.
His gain per cent is-
a. 20
b. 25
c. 30
d. 32
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Ans : Let the S.P. of 100 Oranges be Rs. x.
S.P. of 20 oranges = x/100 *20 = Rs. x/5
C.P. of 100 oranges = x - x/5
= Rs. 4x/5
Reqd. Profit % = x/5 * 100*5/4x %
= 25%
37. 60% of the cost price of an article is equal to 50% of its selling price.Then the percentage of profit or loss on the cost price is-
a. 20% loss
b. 16 2/3% profit
c. 20% profit
d. 10% loss
Ans : Let the cost price be Rs. 100.
S.P * 50/100 = 100*16/100
S.P = 60*100/50
= Rs. 120
Reqd. % profit = (120 100)% = 20%
38. Maninder bought two horses at Rs.40,000 each. He sold one horse at
15% gain, but had to sell the second horse at a loss. If he hand suffered a
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loss of Rs.3,600 on the whole transaction, then the selling price of the
second horse is-
a. Rs.30,000
b. Rs.30,200
c. Rs.30,300
d. Rs.30,400
Ans: C.P. of two horses = 2*40000 = Rs. 80000
and S.P. of two horse = 80000 3600 = Rs. 76400
S.P. of the other horse = 76400 46000 = 30400
39. A fruit-seller buys x guavas for Rs.y and sells y guavas for Rs. x. If x>y,then he made-
a. x2 y2 / xy % loss
b. x2 y2 / xy % gain
c. x2 y2 / y2 % loss
d. x2 y2 / y2 * 100% gain
Ans : C.P. of 1 guava = Rs. y/x [x>y]
and S.P. of 1 guava = Rs. x/y
Reqd. Gain% = x/y y/x/ y/x * 100%
= x2 - y2 /y2 *100%
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40. A jar contain 10 red marbles and 30 green ones. How many red marblesmust be added to the jar so that 60% of the marbles will be red?
a. 25
b. 30
c. 35
d. 40
Ans : Let after adding x red marbles, the red marbles with be 60% of the
total.
(10+x)/ (10 + x) + 30 = 60/100
10 + x/40 + x = 3/5
50 + 5x = 120 + 3x
x = 70/2 = 35
41. If a number multiplied by 25% of itself gives a number which is 200%more than the number, then the number is
a. 12
b. 16
c. 35
d. 24
Ans : Let the number be x.
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x*25x/100 = x + 200x/100
x2/4 = 3x
x2 - 12x = 0
x 12 = 0
x = 12
42. The value of an article depreciates every year at the rate of 10% of its
value. If the present value of the article is Rs.729, then its worth 3 yearsago was-
a. Rs.1250
b. Rs.1000
c. Rs.1125
d. Rs.1200
Ans : Let the worth 3 years ago be Rs. x.
729 = x (1 10/100)3
729 = x*9*9*9/10*10*10
x = Rs. 1000
43. The price of onions has been increased by 50%. In order to keep the
expenditure on onions the same the percentage of reduction in consumptionhas to be-
a. 50%
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b. 33 1/3%
c. 33%
d. 30%
Ans : Reqd. Percentage of reduction
= 50*100/(100 + 50) %
= 5000/150 %
= 33 1/3%
44. A took two loans altogether of Rs.1200 from B and C. B claimed 14%simple interest per annum, while C claimed 15% per annum. The total
interest paid by A in one year was Rs.172. Then, A borrowed-
a. Rs.800 from C
b. Rs.625 from C
c. Rs.400 from B
d. Rs.800 from B
Ans : If A borrowed Rs. x from B. and A borrowed Rs. Rs. (1200 x) from C.
(1200 x)*15*1/100 + x*14*1/100
18000 15x + 14x = 172*100
x = Rs. 800
45. If a regular polygon has each of its angles equal to 3/5 times of tworight angles, then the number of side is-
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a. 3
b. 5
c. 6
d. 8
Ans : If the number of sides a regular polygon be n.
Then (2n-4)/n = 2*3/5
(2n 4)*5 = 6n
n = 5
46. A square is of area 200 sq. m. A new square is formed in such a waythat the length of its diagonal is 2 times of the diagonal of the givensquare. The the area of the new square formed is-
a. 2002 sq.m
b. 4002 sq.m
c. 400 sq.m
d. 800 sq.m
Ans : Length of the diagonal of Ist square
= 2*200
= 20 m
Length of the diagonal of new square = 202m
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91/(10 + x) + 91/(10 x) = 20
91(10 x + 10 + x)(10 + x) (10 x) = 20
91*20 = 20(100 x2)
x2 = 9 = (3)2
x = 3 km/hr
49. A man driving at 3/4th of his original speed reaches his destination 20
minutes later than the usual time. Then the usual time is-
a. 45 minutes
b. 60 minutes
c. 75 minutes
d. 120 minutes
Ans : Let the original speed be x km/hr and the usual time be y hours.
x * y = x(y+1/3)
4y = 3y + 1
y = 1 hr = 60 minutes
50. A motor-boat, travelling at the same speed, can cover 25 km upstreamand 39 km downstream in 8 hours. At the same speed, it can travel 35 km
upstream and 52 km downstream in 11 hours. The speed of the stream is
a. 2 km/hr
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b. 3 km/hr
c. 4 km/hr
d. 5 km/hr
Ans : Let the speeds of motor boat and the stream be x and y km/hrrespectively.
39/x + y + 25/x y = 8 (1)
and 52/x + y + 35/x y = 11 (2)
Solving equations (1) and (2), we get-
100 - 105/x y = 32 33
x y = 5
and x + y = 13
y = 4 km/hr
51. If a sum of money placed at compound interest, compounded annually,doubles itself in 5 years, then the same amount of money will be 8 times ofitself in-
a. 25 years
b. 20 years
c. 15 years
d. 10 years
Ans : Required time = 5log 8/log 2
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= 5*3log 2/log 2
= 15 years
52. A person has left an amount of Rs.1,20,000 to be divided between his 2son aged 14 years and 12 years such that they get equal amounts when
each attains 18 years of age. If the amount gets a simple interest of 5% per
annum, the younger sons share at present is-
a. Rs.48,800
b. Rs.57,600
c. Rs.62,400
d. Rs.84,400
Ans : Let the present share of the younger son be Rs. x.
The share of the elder son = Rs. (120000 x)
x + x*6*5/100
= (120000 x) + (120000 x)*4*5/100
130x/100 = (120000 x)*120/100
13x = 1440000 12x
25x = 1440000
x = Rs. 57600
53. If the simple interest on Rs.x at a rate of a% for m years is same asthat on Rs. y at a rate of a2% for m2 years, then x : y is equal to-
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a. m : a
b. am : 1
c. 1/m : 1/a
d. 1/am : 1
x*a*m/100 = y*a2*m2/100
x/y = am/1
x : y = am : 1
54. Base of a right prism is an equilateral triangle of side 6 cm. If the
volume of the prism is 1083 cc, its height is-
a. 9 cm
b. 10 cm
c. 11 cm
d. 12 cm
Ans : Height of the prism = 1083*4/3*(6)2 = 12cm
55. If a + 1/a + 2 = 0, then the value of (a37 1/a100) is-
a. 0
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b. -2
c. 1
d. 2
Ans : a + 1/a + 2 = 0
a2 + 1 +2a = 0
(a + 1)2 = 0
a +1 = 0
a = -1
a37 -1/a100 = (-1) (1) = -2
56. The value of k for which the graphs of (k-1) x+y-2 = 0 and (2-k) x -3y+ 1 = 0 are parallel is-
a.
b. -1/2
c. 2
d. -2
Ans : (k 1) x + y 2 = 0
y = (1 k) x + 2 .(1)
and (2 k) x 3y 1 = 0
3y = (2 k) x +1
Y = 2 k/3 x + 1/3 .(2)
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m1 = m2
1 k = 2 k/3
3 3k = 2 - k
k = 1/2
57. If a2 + b2 + c2 = 2 (a-b-c) 3, then the value of (a b + c) is-
a. -1
b. 3
c. 1
d. -2
Ans : a2 + b2 + c2 = 2(a b c) 3
a2 - 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
(a 1)2 + (b + 1)2 + (c + 1)2 = 0
a 1 = 0, b + 1 = 0, c + 1 = 0
a = 1, b = -1, c = -1
a + b c = 1 1 + 1 =1
58. If x2 + 3x + 1 = 0, then the value of x3 + 1/x3 is-
a. -18
b. 18
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c. 36
d. -36
Ans : x2 + 3x + 1 = 0
x + 3 + 1/x = 0
x + 1/x = -3
(x + 1/x)3 = (-3)3
x3 + 1/x3 + 3 (-3) = -27
x3 + 1/ x3 = -18
59. If xa, xb, xc = 1, then the value of a3 + b3 + c3 is
a. 9
b. abc
c. a + b + c
d. 3abc
Ans : xa. xb. xc = 1
xa + b + c = x0
a +b + c =0
a3 + b3 + c3 = 3abc
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60. Base of a right pyramid is a square, length of diagonal of the base is
242 m. If the volume of the pyramid is 1728 cu.m, its height is-
a. 7 m
b. 8 m
c. 9 m
d. 10 m
Ans : Area of the base of the pyramid
= (242)2 = 576m2
Height of pyramid + 1728*3/576 = 9m
61. The height of a right circular cone and the radius of its circular base arerespectively 9 cm and 3 cm. The cone is cut by a plane parallel to its base so
as to divide it into two parts. The volume of the frustum (i.e., the lower part)
of the cone is 44 cubic cm. The radius of the upper circular surface of thefrustum (taking = 22-7) is-
a. 312 cm
b. 313 cm
c. 36 cm
d. 320 cm
Ans : Let the radius of the upper circular part of the frustum be r cm.
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(Picture)
Then r/3 = x/9 = AC/AD
x = 3r (where AC = x cm)
/3h(r12 + r1r2+r22 = 44
/3(9 x)*(9 + 3r + r2) = 44
(9 x)*(9 + 3r + r2) = 44*3*7/22 = 42
81 + 27r + 9r2 9x 3rx - r2x = 42 On putting x = 3r,
81 + 27r + 9r2 - 9r2 - 3r3 27r = 42
3r3 = 39
r = 313 cm
62. The ratio of radii of two right circular cylinder is 2 : 3 and their heightsare in the ratio 5 : 4. The ratio of their curved surface area is-
a. 5 : 6
b. 3 : 4
c. 4 : 5
d. 2 : 3
Ans : Required ratio = 2*2r*5h/2*3r*4h = 5 : 6
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63. A solid cylinder has total surface area of 462 sq.cm. Curved surfacearea is 1/3rd of its total surface area. The volume of the cylinder is-
a. 530 cm3
b. 536 cm3
c. 539 cm3
d. 545 cm3
Ans : 2r(r + h) = 462
and 2rh = 1/3*462 = 154
r + h/h = 462/154 =3
r + h = 3h
r = 2h
2*2h2 = 154
h2 = 154*7/22*4 = 49/4
= (7/2)2
h = 7/2 cm
and r = 7 cm
Volume of the cylinder
= 22/7*49*7/2
= 539 cm3
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64. A cylinder and a cone have equal radii of their bases and equal heights.
If their curved surface areas are in the ratio 8 : 5, the ratio of their radiusand height is-
a. 1 : 2
b. 1 : 3
c. 2 : 3
d. 3 : 4
Ans : Let the radius and height of each are r and h respectively.
2rh/rh2 + r2 = 8/5
10h = 8r2 + h2
100h2 =64r2 + 64h2
h2 = 64 r2/36 = (4/3 r)2
h = 4/3r
r : h = 3 : 4
65. A solid is hemispherical at the bottom and conical above. If the surface
areas of the two parts are equal, then the ratio of radius and height of itsconical part is-
a. 1 : 3
b. 1 :1
c. 3 : 1
d. 1 : 3
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Ans :
rl = 2r2
l = 2r
h2 + r2 = 2r
h2 = 3r2
r : h = r/h
= 1 : 3
66. If O is the circumcentre of ABC and OBC = 350, then the BAC isequal to-
a. 550
b. 1100
c. 700
d. 350
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Ans : BOC = 1800 (350 + 350) = 1100
BAC = 1/2 * 1100 = 550
67. If I is the incentre of ABC and BIC = 1350, then ABC is-
a. Acute angled
b. Equilateral
c. Right angled
d. Obtuse angled
Ans :
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BIC = 1350
B/2 + C/2 = 1800 1350 = 450
B + C = 900
A = 1800 (B + C) = 900
i.e., ABC is a right angled.
68. If sin2 (+ /2) is-
a. 1
b. -1
c. 0
d. 0.5
sin2 + sin2 = 2
1 cos2 1 - cos2 = 2
cos2 cos2 = 0
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cos = 0
and cos = 0
= /2 and = /2
cos (+ /2) = cos [/2 + /2 / 2]
= cos /2 = 0
69. The length of a shadow of a vertical tower is 1/3 times its height. Theangle of elevation of the Sun is-
a. 300
b. 450
c. 600
d. 900
Ans :
tan = h/13 h = 3 = tan 600
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(4x 2)2 = 3
4x = 2 + 3
64x3 = (23)3
=8 + 33 + 63 (2 + 3)
= 26 + 153
64x3 + 1/64x3 = (26 + 153) + 1/ (26 + 153)
= (26 + 153) + 26 - 153/676 -675
=52
72. If a, b, c, are three non-zero real numbers such that a + b + c = 0, andb2 ca, then the value of a2 + b2 + c2/ b2 ca is-
a. 3
b. 2
c. 0
d. 1
a + b + c = 0
a + c = -b
a2 + c2 = b2 -2ac
a2 + b2 + c2 = 2b2 2ac
a2 + b2 + c2/ b2 ac = 2
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73. If a4 + a2 b2 + b4 = 8 and a2 + ab + b2 = 4, then the value of ab is-
a. -1
b. 0
c. 2
d. 1
a4 + a2 b2 + b4/ a2 + ab + b2 = 8/4
(a2 + b2)2 (ab) 2/ (a2 + b2 + ab) = 2
a2 ab + b2 = 2 .(1)
and a2 + ab + b2 = 4 ..(2)
2ab = 2
ab = 1
74. If a = 25, b = 15, c = -10, then the value of a3 + b3 + c3 3abc/ (a-b)2 + (b-c)2 + (c-a)2 is-
a. 30
b. -15
c. -30
d. 15
a3 + b3 + c3 3abc
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= (25)3 + (15)3 + (-10)3 3*25*15*(-10)
=15625 + 3375 1000 + 11250 = 29250
and (a - b)2 + (b c)2 + (c a)2
= (10)2 + (25)2 + (-35)2
= (10)2 + 625 + 1225
= 1950
Required value = 29250/1950 =15
75. A, B, C are three points on a circle. The tangent at A meets BCproduced at T, BTA = 400, CAT = 440. The angle subtended by BC at the
centre of the circle is-
a. 840
b. 920
c. 960
d. 1040
Ans : (Picture)
ACB = 400 + 440 = 840
ACO = 900 - 440 = 460 = OAC
OCB = ACB - ACO
= 840 - 460 = 380 = OBC
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BOC = 1800 (OCB + OBC)
= 1800 (380 + 380) = 1040
76. If the length of a chord of a circle at a distance of 12 cm from theCentre is 10 cm, then the diameter of the circle is-
a. 13 cm
b. 15 cm
c. 26 cm
d. 30 cm
Ans : (Picture)
OA = OM2 + AM2
= 122 + 52 = 13
Diameter of the circle = 2*OA
= 2*13 = 26cm
77. In ABC, P and Q are the middle points of the sides AB and ACrespectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR= 2 cm, then BC =
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a. 4 cm
b. 2 cm
c. 12 cm
d. 6 cm
PR/RQ =
But, PR = 2cm
RQ = 2*PR
= 4cm
(Picture)
PQ = PR + RQ
= 2 + 4 = 6 cm
BC = 2*PQ = 12CM
78. If tan tan 2 = 1, then the value of sin2 2 +tan2 is equal to
a.
b. 10/3
c. 3
d. 3
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=1
80. If sin + cos = 17/13, 0
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1. The product of 2 numbers is 1575 and their quotient is 9/7. Then the
sum of the numbers is
a. 74
b. 78
c. 80
d. 90
Ans : Let the numbers be x and y .
xy = 1575
And x/y = 9/7
xy/x/y = 1575/9/7
y2 = 1225
y = 35 and x = 45
The sum of the numbers = 45+35
= 80
2. The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is __
a. 3
b. 6
c. 9
d. 8.2
Ans : (81)3.6 * (9)2.7/(81)4.2 * (3) = (3)14.4 * (3)5.4/(3)16.8 * (3)
= 314.4+5.4-16.8-1
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= 32
= 9
3. 6+6+6+ is equal to
a. 2
b. 5
c. 4
d. 3
Ans : Let 6+6+6+. be x.
x =6+x
x2 = 6+x
x2 + x 6 = 0
(x-3) (x+2) = 0
x = 3
4. The sum of the squares of two natural consecutive odd numbers is 394.The sum of the numbers is
a. 24
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b. 32
c. 40
d. 28
Ans : Let the consecutive odd numbers be x and (x+2)
x2 + (x + 2)2 = 394
x2 + x2 + 4x + 4 = 394
2 x2 +4x 390 = 0
x2 + 2x 195 = 0
(x +15) (x-13) = 0
x = 13
Required sum = 13 +15 =28
5. When (6767 +67) is divided by 68, the remainder is-
a. 1
b. 63
c. 66
d. 67
Ans: (6767+ 67) = 67(6766 + 166)
As 66 is an even number
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6766 is an even number
(6766 + 1) is perfectly divisible by (67 + 1)
i.e. 68
The remainder = 67
6. In a division sum, the divisor is 4 times the quotient and twice theremainder. If a and b are respectively the divisor and the dividend then-
a. 4b-a2 /a =3
b. 4b-2a /a2 =2
c. (a+1)2 = 4b
d. A(a+2)/b = 4
Ans : As divisor is a, and dividend is b.
Quotient = a/4
And Remainder = a/2
b = a * a/4 + a/2
4b = a2 + 2a
a(a+2)/b = 4
7. If 738 A6A is divisible by 11, then the value of A is-
a. 6
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b. 3
c. 9
d. 1
Ans : As 738A6 A is divisible by 11.
A + A + 3 = 6 + 8 + 7
A = 9
8. The east positive integer that should be subtracted from 3011 * 3012 sothat the difference is perfect square is-
a. 3009
b. 3010
c. 3011
d. 3012
Ans : 3011 * 3012 = 3011 (3011 + 1)
= (3011)2 + 3011
Required least number = 3011
9. P, Q, R are employed to do a work for Rs. 5750. P and Q together
finished 19/23 of work and Q and R together finished 8/23 of work. Wage of
Q, in rupees, is-
a. 2850
b. 3750
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c. 2750
d. 1000
Ans : Work done by Q = 19/23 + 8/23 1
4/23
Wage of Q = 4/23 * 5750
= Rs. 1000
10. A can do a piece of work in 24 day, B in 32 days and C in 64 days. Allbegin to do it together, but A leaves after 6 days and B leaves 6 days before
the completion of the work. How many days did the work last?
a. 15
b. 20
c. 18
d. 30
Ans : Work done by A = 6/24 =
Work done by B = (x-6)/32
(where x is no. of days in which work is competed)
+ x 6/32 + x/64 = 1
16 + 24 12 + x /64 = 1
3x + 4 = 64
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x = 60/3 = 20 days
11. The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-
a. 1
b. 2
c. 3
d. 4
Ans : The square root of
[(0.75)3/1 0.75 + {0.75 + (0.75)2 + 1}]
= 1.6875 + 2.3125
=4
= 2
12. Given that 4096 = 64, the value of 4096 + 40.96 +0.004096 is-
a. 70.4
b. 70.464
c. 71.104
d. 71.4
Ans : Given Exp. = 4096 + 40.96 +0.004096
= 64 + 6.4 + 0.064
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= 70.464
13. By selling an article at 3/4th of the marked price, there is a gain of
25%. The ratio of the marked price and the cost price is-
a. 5 : 3
b. 3 : 5
c. 3 : 4
d. 4 : 3
Ans : Let of M.P. be Rs. x.
S.P. = Rs.3x/4
and C.P. = 3x/4 * 100/125
= Rs.3x/5
required ratio = x: 3x/5
= 5:3
14. A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in
the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, themonthly income of B is-
a. Rs.7,000
b. Rs.14,000
c. Rs.5,000
d. Rs.10,000
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x : y = 3 : 2
16. A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hours
respectively, and C can empty it in 1 hour. If the pipes are opened at 3p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will be
empty at-
a. 7.12 p.m.
b. 7.15 p.m.
c. 7.10 p.m.
d. 7.18 p.m.
Ans : Let the cistern be emptied at x p.m.
x -3/3 + x 4/4 = x - 5/1
4x 12 + 3x 12/12 = x 5/1
7x 24 = 12x 60
5x = 36
x = 36/5
= 7 hr. + 12 min.
= 7.12 p.m.
17. If A works alone, he would take 4 days more to complete the job than if
both A and B worked together. If B worked alone, he would take 16 daysmore to complete the job than if A and B work together. How many days
would they take to complete the work if both of them worked together?
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a. 10 days
b. 12 days
c. 6 days
d. 8 days
Let x days are taken when they work together.
Time taken by A to complete the work = (x + 4) days
And Time taken by B to complete the work = (x + 16) days
1/x = 1/x + 4 + 1/x + 16
1/x = x + 16 + x + 4/(x + 4) (x +16)
2x2 + 20x = x2 + 20x +64
x2 = 64 (8)2
x = 8 days
18. 250 men can finish a work in 20 days working 5 hours a day. To finish
the work within 10 days working 8 hours a day, the minimum number ofmen required is-
a. 310
b. 300
c. 313
d. 312
Ans : Required no. of men = 250 * 5 * 20/8 * 10
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c. 16 2/3%
d. 16 1/3%
Ans : Let the M.P. be Rs.100.
S.P = (100-40) = Rs.60
and C. P. = 60 * 100/(100-30) = Rs.600/7
Reqd. % profit = 100-600/7 /600/7 * 100%
= (700 600)/7 * 600 * 100 * 7%
= 16 2/3%
21. Successive discount of 10% , 20% and 50% will be equivalent to a
single discount of-
a. 36%
b. 64%
c. 80%
d. 56%
Ans : Equivalent to a single discount
= [100 - (100 10) (100 20) (100 50)/100*100]%
= [100 - 90*80*50/10000]%
= [100-36]%
= 64%
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22. A retailer offers the following discount schemes for buyers on an article-
I. Two successive discounts of 10%
II. A discount of 12% followed by a discount of 8%.
III. Successive discounts of 15% and 5%
IV. A discount of 20%
The selling price will be minimum under the scheme-
a. I
b. II
c. III
d. IV
Ans : From (i) single discount = [10 + 10 10*10/100] % = 19%
From (ii) single discount = [12 + 8 -12*8/100] % = 19.04%
From (iii) single discount = [15 + 5 15*5/100] % = 19.25%
From (iv) single discount = 20%
The S.P. will be minimum under the scheme IV.
23. Of three numbers, the second is thrice the first and the third number is
three-fourth of the first. If the average of the three numbers is 114, thelargest number is
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a. 72
b. 216
c. 354
d. 726
Ans : Let the first number be x.
Second number = 3x and Third number = 3x/4
x + 3x + 3x/4 = 3*114
19x/4 = 342
x = 342*4/19 = 72
The largest number = 3*72
= 216
24. A car covers 1/5 of the distance from A to B at the speed of 8 km/hour,
1/10 of the distance at 25 km per hour and the remaining at the speed of 20km per hour. Find the average speed of the whole journey-
a. 12.625 km/hr
b. 13.625 km/hr
c. 14.625 km/hr
d. 15.625 km/hr
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Ans : If the whole journey be x km. The total time taken
= (x/5/8 + x/10/25 + 7x/10/20) hrs
= (x/40 + x/250 + 7x/200) hrs
= 25x + 4x + 35x/1000
= 64x/1000 hrs
Average speed = x/64x/1000
= 15.625 km/hr
25. The average of 3 numbers is 154. The first number is twice the second
and the second number is twice the third. The first number is-
a. 264
b. 132
c. 88
d. 66
Ans : Let the first number be x.
Second number = x/2 and Third number = x/4
x + x/2 + x/4 = 3 x 154
7x/4 = 462
x = 462*4/7
=264
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26. The average salary of all the staff in an office of a corporate house is
Rs. 5,000. The average salary of the officers is Rs. 14,000 and that of therest is Rs. 4,000. If the total number of staff is 500, the number of officers is
a. 10
b. 15
c. 25
d. 50
Ans : Let the number of officers be x.
5000*500 = 14000x + 4000(500-x)
2500000 =14000x + 2000000 4000x
x = 500000/10000
= 50
27. The average marks of 40 students in an English exam are 72. Later it is
found that three marks 64, 62 and 84 were wrongly entered as 60, 65 and73. The average after mistakes were rectified is-
a. 70
b. 72
c. 71.9
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29. In a laboratory, two bottles contain mixture of acid and water in theratio 2 : 5 in the first bottle and 7 : 3 in the second. The ratio in which thecontents of these two bottles be mixed such that the new mixture has acid
and water in the ratio 2 : 3 is-
a. 4 : 15
b. 9 : 8
c. 21 : 8
d. 1 : 2
Ans : Quantity of acid in first bottle = 2/7 x mix.
and Quantity of acid in second bottle = 7/10 x mix.
If x and 1 volumes are taken from I and II bottle respectively to form new
mixture.
Then, (2/7 x + 7/10 * 1)/(5x/7 +3/10 * 1) = 2/3
6x/7 21/10 = 10x/7 +6/10
4x/7 = 15/10
x = 15/10*7/4 = 21/8
Required ratio = x : 1
= 21 : 8
30. A mixture contains 80% acid and rest water. Part of the mixture thatshould be removed and replaced by same amount of water to make the ratio
of acid and water 4 : 3 is-
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a. 1/3 rd
b. 3/7 th
c. 2/3 rd
d. 2/7 th
Ans : Let the initial wt. of mixture be 1 kg and x kg of mixture is taken out
and replaced by same amount of water.
Amt. of acid/Amt. of water = 0.8 0.8x/ (0.2 0.2x + x) = 4/3
2.4 2.4x = 0.8 + 3.2x
5.6x = 1.6
x = 1.6/5.6 = 2/7th part
31. An employer reduces the number of his employees in the ratio 9 : 8 and
increases their wages in the ratio 14 : 15. If the original wage bill was Rs.
189,900, find the ratio in which the wage bill is decreased-
a. 20 : 21
b. 21 : 20
c. 20 : 19
d. 19 : 21
Ans : Let the initial number of employees be 9x and the employer gives Rs.
14y as wage to each.
9x * 14y =18900
xy = 150 and The later bill = 8x*15y = 120xy
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= 120*150 = 18000
Required ratio = 18000 : 18900
= 20 : 21
32. The batting average for 40 innings of a cricketer is 50 runs. His highest
score exceeds his lowest score by 172 runs. If these two innings areexcluded, the average of the remaining 38 innings is 48 runs. The highestscore of the player is-
a. 165
b. 170
c. 172
d. 174
Ans : Let the max. number of runs be x.
The lowest score = (x-172)
40*50 = 38*48 + x + (x-172)
2000 = 1824 + 2x 172
x= 174
33. Walking at 3 km per hour, Pintu reaches his school 5 minutes late. If hewalks at 4 km per hour he will be 5 minutes early. The distance of Pintusschool from his house is-
a. 1 Km
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Ans : Let the S.P. of 100 Oranges be Rs. x.
S.P. of 20 oranges = x/100 *20 = Rs. x/5
C.P. of 100 oranges = x - x/5
= Rs. 4x/5
Reqd. Profit % = x/5 * 100*5/4x %
= 25%
37. 60% of the cost price of an article is equal to 50% of its selling price.Then the percentage of profit or loss on the cost price is-
a. 20% loss
b. 16 2/3% profit
c. 20% profit
d. 10% loss
Ans : Let the cost price be Rs. 100.
S.P * 50/100 = 100*16/100
S.P = 60*100/50
= Rs. 120
Reqd. % profit = (120 100)% = 20%
38. Maninder bought two horses at Rs.40,000 each. He sold one horse at
15% gain, but had to sell the second horse at a loss. If he hand suffered a
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loss of Rs.3,600 on the whole transaction, then the selling price of the
second horse is-
a. Rs.30,000
b. Rs.30,200
c. Rs.30,300
d. Rs.30,400
Ans: C.P. of two horses = 2*40000 = Rs. 80000
and S.P. of two horse = 80000 3600 = Rs. 76400
S.P. of the other horse = 76400 46000 = 30400
39. A fruit-seller buys x guavas for Rs.y and sells y guavas for Rs. x. If x>y,then he made-
a. x2 y2 / xy % loss
b. x2 y2 / xy % gain
c. x2 y2 / y2 % loss
d. x2 y2 / y2 * 100% gain
Ans : C.P. of 1 guava = Rs. y/x [x>y]
and S.P. of 1 guava = Rs. x/y
Reqd. Gain% = x/y y/x/ y/x * 100%
= x2 - y2 /y2 *100%
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40. A jar contain 10 red marbles and 30 green ones. How many red marblesmust be added to the jar so that 60% of the marbles will be red?
a. 25
b. 30
c. 35
d. 40
Ans : Let after adding x red marbles, the red marbles with be 60% of the
total.
(10+x)/ (10 + x) + 30 = 60/100
10 + x/40 + x = 3/5
50 + 5x = 120 + 3x
x = 70/2 = 35
41. If a number multiplied by 25% of itself gives a number which is 200%more than the number, then the number is
a. 12
b. 16
c. 35
d. 24
Ans : Let the number be x.
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b. 33 1/3%
c. 33%
d. 30%
Ans : Reqd. Percentage of reduction
= 50*100/(100 + 50) %
= 5000/150 %
= 33 1/3%
44. A took two loans altogether of Rs.1200 from B and C. B claimed 14%simple interest per annum, while C claimed 15% per annum. The total
interest paid by A in one year was Rs.172. Then, A borrowed-
a. Rs.800 from C
b. Rs.625 from C
c. Rs.400 from B
d. Rs.800 from B
Ans : If A borrowed Rs. x from B. and A borrowed Rs. Rs. (1200 x) from C.
(1200 x)*15*1/100 + x*14*1/100
18000 15x + 14x = 172*100
x = Rs. 800
45. If a regular polygon has each of its angles equal to 3/5 times of tworight angles, then the number of side is-
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a. 3
b. 5
c. 6
d. 8
Ans : If the number of sides a regular polygon be n.
Then (2n-4)/n = 2*3/5
(2n 4)*5 = 6n
n = 5
46. A square is of area 200 sq. m. A new square is formed in such a waythat the length of its diagonal is 2 times of the diagonal of the givensquare. The the area of the new square formed is-
a. 2002 sq.m
b. 4002 sq.m
c. 400 sq.m
d. 800 sq.m
Ans : Length of the diagonal of Ist square
= 2*200
= 20 m
Length of the diagonal of new square = 202m
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Area of the new square = *(20.2)2 = 400 sq. m
47. The heights of a cone, cylinder and hemisphere are equal. If their radii
are in the ratio 2 : 3 : 1, then the ratio of their volumes is-
a. 2 : 9 : 2
b. 4 : 9 : 1
c. 4 : 27 : 2
d. 2 : 3 : 1
Ans : Ratio of their volumes [cone : cylinder : hemisphere]
= 1/3(2)2h : (3)2*h : 2/3(1)2.h
= 4/3 : 9 : 2/3 = 4 : 27 : 2
48. A motor-boat can travel at 10 km/hr in still water. It travelled 91 km
downstream in a river and then returned to the same place, takingaltogether 2 hours. Find the rate of flow of river-
a. 3 km/hr
b. 4 km/hr
c. 2 km/hr
d. 5 km/hr
Ans : Let the rate of flow of river be x km/hr.
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b. 3 km/hr
c. 4 km/hr
d. 5 km/hr
Ans : Let the speeds of motor boat and the stream be x and y km/hrrespectively.
39/x + y + 25/x y = 8 (1)
and 52/x + y + 35/x y = 11 (2)
Solving equations (1) and (2), we get-
100 - 105/x y = 32 33
x y = 5
and x + y = 13
y = 4 km/hr
51. If a sum of money placed at compound interest, compounded annually,doubles itself in 5 years, then the same amount of money will be 8 times ofitself in-
a. 25 years
b. 20 years
c. 15 years
d. 10 years
Ans : Required time = 5log 8/log 2
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= 5*3log 2/log 2
= 15 years
52. A person has left an amount of Rs.1,20,000 to be divided between his 2son aged 14 years and 12 years such that they get equal amounts when
each attains 18 years of age. If the amount gets a simple interest of 5% per
annum, the younger sons share at present is-
a. Rs.48,800
b. Rs.57,600
c. Rs.62,400
d. Rs.84,400
Ans : Let the present share of the younger son be Rs. x.
The share of the elder son = Rs. (120000 x)
x + x*6*5/100
= (120000 x) + (120000 x)*4*5/100
130x/100 = (120000 x)*120/100
13x = 1440000 12x
25x = 1440000
x = Rs. 57600
53. If the simple interest on Rs.x at a rate of a% for m years is same asthat on Rs. y at a rate of a2% for m2 years, then x : y is equal to-
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a. m : a
b. am : 1
c. 1/m : 1/a
d. 1/am : 1
x*a*m/100 = y*a2*m2/100
x/y = am/1
x : y = am : 1
54. Base of a right prism is an equilateral triangle of side 6 cm. If the
volume of the prism is 1083 cc, its height is-
a. 9 cm
b. 10 cm
c. 11 cm
d. 12 cm
Ans : Height of the prism = 1083*4/3*(6)2 = 12cm
55. If a + 1/a + 2 = 0, then the value of (a37 1/a100) is-
a. 0
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b. -2
c. 1
d. 2
Ans : a + 1/a + 2 = 0
a2 + 1 +2a = 0
(a + 1)2 = 0
a +1 = 0
a = -1
a37 -1/a100 = (-1) (1) = -2
56. The value of k for which the graphs of (k-1) x+y-2 = 0 and (2-k) x -3y+ 1 = 0 are parallel is-
a.
b. -1/2
c. 2
d. -2
Ans : (k 1) x + y 2 = 0
y = (1 k) x + 2 .(1)
and (2 k) x 3y 1 = 0
3y = (2 k) x +1
Y = 2 k/3 x + 1/3 .(2)
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m1 = m2
1 k = 2 k/3
3 3k = 2 - k
k = 1/2
57. If a2 + b2 + c2 = 2 (a-b-c) 3, then the value of (a b + c) is-
a. -1
b. 3
c. 1
d. -2
Ans : a2 + b2 + c2 = 2(a b c) 3
a2 - 2a + 1 + b2 + 2b + 1 + c2 + 2c + 1 = 0
(a 1)2 + (b + 1)2 + (c + 1)2 = 0
a 1 = 0, b + 1 = 0, c + 1 = 0
a = 1, b = -1, c = -1
a + b c = 1 1 + 1 =1
58. If x2 + 3x + 1 = 0, then the value of x3 + 1/x3 is-
a. -18
b. 18
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60. Base of a right pyramid is a square, length of diagonal of the base is
242 m. If the volume of the pyramid is 1728 cu.m, its height is-
a. 7 m
b. 8 m
c. 9 m
d. 10 m
Ans : Area of the base of the pyramid
= (242)2 = 576m2
Height of pyramid + 1728*3/576 = 9m
61. The height of a right circular cone and the radius of its circular base arerespectively 9 cm and 3 cm. The cone is cut by a plane parallel to its base so
as to divide it into two parts. The volume of the frustum (i.e., the lower part)
of the cone is 44 cubic cm. The radius of the upper circular surface of thefrustum (taking = 22-7) is-
a. 312 cm
b. 313 cm
c. 36 cm
d. 320 cm
Ans : Let the radius of the upper circular part of the frustum be r cm.
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(Picture)
Then r/3 = x/9 = AC/AD
x = 3r (where AC = x cm)
/3h(r12 + r1r2+r22 = 44
/3(9 x)*(9 + 3r + r2) = 44
(9 x)*(9 + 3r + r2) = 44*3*7/22 = 42
81 + 27r + 9r2 9x 3rx - r2x = 42 On putting x = 3r,
81 + 27r + 9r2 - 9r2 - 3r3 27r = 42
3r3 = 39
r = 313 cm
62. The ratio of radii of two right circular cylinder is 2 : 3 and their heightsare in the ratio 5 : 4. The ratio of their curved surface area is-
a. 5 : 6
b. 3 : 4
c. 4 : 5
d. 2 : 3
Ans : Required ratio = 2*2r*5h/2*3r*4h = 5 : 6
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63. A solid cylinder has total surface area of 462 sq.cm. Curved surfacearea is 1/3rd of its total surface area. The volume of the cylinder is-
a. 530 cm3
b. 536 cm3
c. 539 cm3
d. 545 cm3
Ans : 2r(r + h) = 462
and 2rh = 1/3*462 = 154
r + h/h = 462/154 =3
r + h = 3h
r = 2h
2*2h2 = 154
h2 = 154*7/22*4 = 49/4
= (7/2)2
h = 7/2 cm
and r = 7 cm
Volume of the cylinder
= 22/7*49*7/2
= 539 cm3
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64. A cylinder and a cone have equal radii of their bases and equal heights.
If their curved surface areas are in the ratio 8 : 5, the ratio of their radiusand height is-
a. 1 : 2
b. 1 : 3
c. 2 : 3
d. 3 : 4
Ans : Let the radius and height of each are r and h respectively.
2rh/rh2 + r2 = 8/5
10h = 8r2 + h2
100h2 =64r2 + 64h2
h2 = 64 r2/36 = (4/3 r)2
h = 4/3r
r : h = 3 : 4
65. A solid is hemispherical at the bottom and conical above. If the surface
areas of the two parts are equal, then the ratio of radius and height of itsconical part is-
a. 1 : 3
b. 1 :1
c. 3 : 1
d. 1 : 3
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BAC = 1/2 * 1100 = 550
67. If I is the incentre of ABC and BIC = 1350, then ABC is-
a. Acute angled
b. Equilateral
c. Right angled
d. Obtuse angled
Ans : (Picture)
BIC = 1350
B/2 + C/2 = 1800 1350 = 450
B + C = 900
A = 1800 (B + C) = 900
i.e., ABC is a right angled.
68. If sin2 (+ /2) is-
a. 1
b. -1
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c. 0
d. 0.5
sin2 + sin2 = 2
1 cos2 1 - cos2 = 2
cos2 cos2 = 0
cos = 0
and cos = 0
= /2 and = /2
cos (+ /2) = cos [/2 + /2 / 2]
= cos /2 = 0
69. The length of a shadow of a vertical tower is 1/3 times its height. Theangle of elevation of the Sun is-
a. 300
b. 450
c. 600
d. 900
Ans : (Picture)
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tan = h/13 h = 3 = tan 600
70. The graphs of x +2y =3 and 3x-2y = 1 meet the Y-axis at two points
having distance-
a. 8/3 units
b. 4/3 units
c. 1 unit
d. 2 units
Ans : When the graphs meet the Y-axis at two points.
Then, [x + 2y = 3] at x = 0 [0, y1 =3/2]
[3x - 2y = 1] at x = 0
and i.e., [0, y2 = -1/2]
Required distance = (y1 y2)
= 3/2 (- ) = 2 units
71. If x+1/16x = 1, then the value of 64x3 + 1/64x3 is-
a. 4
b. 52
c. 64
d. 76
x + 1/16x = 1
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16x2 16x + 1 =0
16x2 16x + 4 = 3
(4x 2)2 = 3
4x = 2 + 3
64x3 = (23)3
=8 + 33 + 63 (2 + 3)
= 26 + 153
64x3 + 1/64x3 = (26 + 153) + 1/ (26 + 153)
= (26 + 153) + 26 - 153/676 -675
=52
72. If a, b, c, are three non-zero real numbers such that a + b + c = 0, and
b2 ca, then the value of a2 + b2 + c2/ b2 ca is-
a. 3
b. 2
c. 0
d. 1
a + b + c = 0
a + c = -b
a2 + c2 = b2 -2ac
a2 + b2 + c2 = 2b2 2ac
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a2 + b2 + c2/ b2 ac = 2
73. If a4 + a2 b2 + b4 = 8 and a2 + ab + b2 = 4, then the value of ab is-
a. -1
b. 0
c. 2
d. 1
a4 + a2 b2 + b4/ a2 + ab + b2 = 8/4
(a2 + b2)2 (ab) 2/ (a2 + b2 + ab) = 2
a2 ab + b2 = 2 .(1)
and a2 + ab + b2 = 4 ..(2)
2ab = 2
ab = 1
74. If a = 25, b = 15, c = -10, then the value of a3 + b3 + c3 3abc/ (a-b)2 + (b-c)2 + (c-a)2 is-
a. 30
b. -15
c. -30
d. 15
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a3 + b3 + c3 3abc
= (25)3 + (15)3 + (-10)3 3*25*15*(-10)
=15625 + 3375 1000 + 11250 = 29250
and (a - b)2 + (b c)2 + (c a)2
= (10)2 + (25)2 + (-35)2
= (10)2 + 625 + 1225
= 1950
Required value = 29250/1950 =15
75. A, B, C are three points on a circle. The tangent at A meets BC
produced at T, BTA = 400, CAT = 440. The angle subtended by BC at the
centre of the circle is-
a. 840
b. 920
c. 960
d. 1040
Ans : (Picture)
ACB = 400 + 440 = 840
ACO = 900 - 440 = 460 = OAC
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OCB = ACB - ACO
= 840 - 460 = 380 = OBC
BOC = 1800 (OCB + OBC)
= 1800 (380 + 380) = 1040
76. If the length of a chord of a circle at a distance of 12 cm from theCentre is 10 cm, then the diameter of the circle is-
a. 13 cm
b. 15 cm
c. 26 cm
d. 30 cm
Ans : (Picture)
OA = OM2 + AM2
= 122 + 52 = 13
Diameter of the circle = 2*OA
= 2*13 = 26cm
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77. In ABC, P and Q are the middle points of the sides AB andACrespectively. R is a point on the segment PQ such that PR : RQ = 1 : 2. If PR= 2 cm, then BC =
a. 4 cm
b. 2 cm
c. 12 cm
d. 6 cm
PR/RQ =
But, PR = 2cm
RQ = 2*PR
= 4cm
(Picture)
PQ = PR + RQ
= 2 + 4 = 6 cm
BC = 2*PQ = 12CM
78. If tan tan 2 = 1, then the value of sin2 2 + tan2 is equal to
a.
b. 10/3
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c. 3
d. 3
tan * tan 2= 1
tan * 2 tan /1 tan2 = 1
2 tan2 = 1 - tan2
3 tan2 = 1
tan = 1/3 = tan 300
= 300
sin2 2+ tan2 2= sin2 600 + tan2 600
= + 3
=3
79. The value of cot
/20 cot 3
/20 cot 5
/20 cot 7
/20 cot 9
/20 is-
a. -1
b.
c. 0
d. 1
Ans : Given Exp.
= cot /20. cot 3/20. cot 5/20. cot 7/20. cot 9/20
= cot 90. cot 270. cot 450. cot 630. cot 810
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= cot 90. cot 270*1*tan 270. tan 90.
= cot 90. cot 270*1*1/ cot 270*1/ cot 90
=1
80. If sin + cos = 17/13, 0
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Arithmetical Ability
1. The product of 2 numbers is 1575 and their quotient is 9/7. Then the
sum of the numbers is
a. 74
b. 78
c. 80
d. 90
Ans : Let the numbers be x and y .
xy = 1575
And x/y = 9/7
xy/x/y = 1575/9/7
y2 = 1225
y = 35 and x = 45
The sum of the numbers = 45+35
= 80
2. The value of (81)3.6 * (9)2.7/ (81)4.2 * (3) is __
a. 3
b. 6
c. 9
d. 8.2
Ans : (81)3.6 * (9)2.7/(81)4.2 * (3) = (3)14.4 * (3)5.4/(3)16.8 * (3)
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= 314.4+5.4-16.8-1
= 32
= 9
3. 6+6+6+ is equal to
a. 2
b. 5
c. 4
d. 3
Ans : Let 6+6+6+. be x.
x =6+x
x2 = 6+x
x2 + x 6 = 0
(x-3) (x+2) = 0
x = 3
4. The sum of the squares of two natural consecutive odd numbers is 394.
The sum of the numbers is
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a. 24
b. 32
c. 40
d. 28
Ans : Let the consecutive odd numbers be x and (x+2)
x2 + (x + 2)2 = 394
x2 + x2 + 4x + 4 = 394
2 x2 +4x 390 = 0
x2 + 2x 195 = 0
(x +15) (x-13) = 0
x = 13
Required sum = 13 +15 =28
5. When (6767 +67) is divided by 68, the remainder is-
a. 1
b. 63
c. 66
d. 67
Ans: (6767+ 67) = 67(6766 + 166)
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b. 3750
c. 2750
d. 1000
Ans : Work done by Q = 19/23 + 8/23 1
4/23
Wage of Q = 4/23 * 5750
= Rs. 1000
10. A can do a piece of work in 24 day, B in 32 days and C in 64 days. Allbegin to do it together, but A leaves after 6 days and B leaves 6 days before
the completion of the work. How many days did the work last?
a. 15
b. 20
c. 18
d. 30
Ans : Work done by A = 6/24 =
Work done by B = (x-6)/32
(where x is no. of days in which work is competed)
+ x 6/32 + x/64 = 1
16 + 24 12 + x /64 = 1
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3x + 4 = 64
x = 60/3 = 20 days
11. The square root of (0.75)3 /1-0.75 + [0.75 + 90.75)2 +1] is-
a. 1
b. 2
c. 3
d. 4
Ans : The square root of
[(0.75)3/1 0.75 + {0.75 + (0.75)2 + 1}]
= 1.6875 + 2.3125
=4
= 2
12. Given that 4096 = 64, the value of 4096 + 40.96 +0.004096 is-
a. 70.4
b. 70.464
c. 71.104
d. 71.4
Ans : Given Exp. = 4096 + 40.96 +0.004096
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= 64 + 6.4 + 0.064
= 70.464
13. By selling an article at 3/4th of the marked price, there is a gain of25%. The ratio of the marked price and the cost price is-
a. 5 : 3
b. 3 : 5
c. 3 : 4
d. 4 : 3
Ans : Let of M.P. be Rs. x.
S.P. = Rs.3x/4
and C.P. = 3x/4 * 100/125
= Rs.3x/5
required ratio = x: 3x/5
= 5:3
14. A and B earn in the ratio 2:1. They spend in the ratio 5:3 and save in
the ratio 4:1. If the total monthly savings of both A and B are Rs.5,000, themonthly income of B is-
a. Rs.7,000
b. Rs.14,000
c. Rs.5,000
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d. Rs.10,000
Ans : Let the monthly income of B be Rs. x.
Monthly income of A = Rs. 2x and
Saving of A =5000 * 4/(4 + 1)
= Rs. 4000
Saving of B = Rs.1000
2x 4000/x-1000 = 5/3
6x 12000 = 5x 5000
x = Rs.7000
15. The ratio of the sum of two numbers and their difference is 5:1. Theratio of the greater number to the smaller number is-
a. 2 : 3
b. 3 : 2
c. 5 : 1
d. 1 : 5
Ans : Let the numbers be x and y.
x + y/ x y = 5/1
5x 5y = x + y
4x = 6y
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x/y = 6/4
x : y = 3 : 2
16. A cistern has 3 pipes A, B and C. A and B can fill it in 3 and 4 hoursrespectively, and C can empty it in 1 hour. If the pipes are opened at 3
p.m., 4 p.m. and 5 p.m. respectively on the same day, the cistern will beempty at-
a. 7.12 p.m.
b. 7.15 p.m.
c. 7.10 p.m.
d. 7.18 p.m.
Ans : Let the cistern be emptied at x p.m.
x -3/3 + x 4/4 = x - 5/1
4x 12 + 3x 12/12 = x 5/1
7x 24 = 12x 60
5x = 36
x = 36/5
= 7 hr. + 12 min.
= 7.12 p.m.
17. If A works alone, he would take 4 days more to complete the job than ifboth A and B worked together. If B worked alone, he would take 16 days
more to complete the job than if A and B work together. How many dayswould they take to complete the work if both of them worked together?
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a. 10 days
b. 12 days
c. 6 days
d. 8 days
Let x days are taken when they work together.
Time taken by A to complete the work = (x + 4) days
And Time taken by B to complete the work = (x + 16) days
1/x = 1/x + 4 + 1/x + 16
1/x = x + 16 + x + 4/(x + 4) (x +16)
2x2 + 20x = x2 + 20x +64
x2 = 64 (8)2
x = 8 days
18. 250 men can finish a work in 20 days working 5 hours a day. To finish
the work within 10 days working 8 hours a day, the minimum number ofmen required is-
a. 310
b. 300
c. 313
d. 312
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Ans : Required no. of men = 250 * 5 * 20/8 * 10
=312.5
313
19. 2 men and 5 women can do a work in 12 days. 5 men 2 women can dothat work in 9 days. Only 3 women can finish the same work in-
a. 36 days
b. 21 days
c. 30 days
d. 42 days
(2m + 5w) * 12 = (5m + 2w) * 9
24m + 60w = 45m + 18w
21m = 42w
1m = 2w
2m + 5w = 9w
required no. of days = 9 * 12/3
= 36
20. While selling, a businessman allows 40% discount on the marked priceand there is a loss of 30%. If it is sold at the marked price, profit per cent
will be
a. 10%
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b. 20%
c. 16 2/3%
d. 16 1/3%
Ans : Let the M.P. be Rs.100.
S.P = (100-40) = Rs.60
and C. P. = 60 * 100/(100-30) = Rs.600/7
Reqd. % profit = 100-600/7 /600/7 * 100%
= (700 600)/7 * 600 * 100 * 7%
= 16 2/3%
21. Successive discount of 10% , 20% and 50% will be equivalent to asingle discount of-
a. 36%
b. 64%
c. 80%
d. 56%
Ans : Equivalent to a single discount
= [100 - (100 10) (100 20) (100 50)/100*100]%
= [100 - 90*80*50/10000]%
= [100-36]%
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= 64%
22. A retailer offers the following discount schemes for buyers on an article-
I. Two successive discounts of 10%
II. A discount of 12% followed by a discount of 8%.
III. Successive discounts of 15% and 5%
IV. A discount of 20%
The selling price will be minimum under the scheme-
a. I
b. II
c. III
d. IV
Ans : From (i) single discount = [10 + 10 10*10/100] % = 19%
From (ii) single discount = [12 + 8 -12*8/100] % = 19.04%
From (iii) single discount = [15 + 5 15*5/100] % = 19.25%
From (iv) single discount = 20%
The S.P. will be minimum under the scheme IV.
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23. Of three numbers, the second is thrice the first and the third number is
three-fourth of the first. If the average of the three numbers is 114, thelargest number is
a. 72
b. 216
c. 354
d. 726
Ans : Let the first number be x.
Second number = 3x and Third number = 3x/4
x + 3x + 3x/4 = 3*114
19x/4 = 342
x = 342*4/19 = 72
The largest number = 3*72
= 216
24. A car covers 1/5 of the distance from A to B at the speed of 8 km/hour,
1/10 of the distance at 25 km per hour and the remaining at the speed of 20km per hour. Find the average speed of the whole journey-
a. 12.625 km/hr
b. 13.625 km/hr
c. 14.625 km/hr
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d. 15.625 km/hr
Ans : If the whole journey be x km. The total time taken
= (x/5/8 + x/10/25 + 7x/10/20) hrs
= (x/40 + x/250 + 7x/200) hrs
= 25x + 4x + 35x/1000
= 64x/1000 hrs
Average speed = x/64x/1000
= 15.625 km/hr
25. The average of 3 numbers is 154. The first number is twice the second
and the second number is twice the third. The first number is-
a. 264
b. 132
c. 88
d. 66
Ans : Let the first number be x.
Second number = x/2 and Third number = x/4
x + x/2 + x/4 = 3 x 154
7x/4 = 462
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x = 462*4/7
=264
26. The average salary of all the staff in an office of a corporate house is
Rs. 5,000. The average salary of the officers is Rs. 14,000 and that of therest is Rs. 4,000. If the total number of staff is 500, the number of officers is
a. 10
b. 15
c. 25
d. 50
Ans : Let the number of officers be x.
5000*500 = 14000x + 4000(500-x)
2500000 =14000x + 2000000 4000x
x = 500000/10000
= 50
27. The average marks of 40 students in an English exam are 72. Later it isfound that three marks 64, 62 and 84 were wrongly entered as 60, 65 and
73. The average after mistakes were rectified is-
a. 70
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b. 72
c. 71.9
d. 72.1
Ans : Correct average
= 40*72 + (64 + 62 +84) 68 65 73/40
= 2880 + 210 206/40 = 2884/40
= 72.1
28. A and B are two alloys of gold and copper prepared by mixing metals inthe ratio 7:2 and 7:11 respectively. If equal quantities of the alloys are
melted to form a third alloy C, the ratio of gold and copper in C will be-
a. 5 : 7
b. 5 : 9
c. 7 : 5
d. 9 : 5
Ans : Quantity of gold in A = 7/9* wt. of A
Quantity of gold in B = 7/18* wt. of B
If 1 kg of each A and B are mixed to form third alloys C.
Then quantity of gold in 2 kg C = 7/9 + 7/18
= 7/6 kg
And Quantity of copper in 2 kg C = 2 7/6
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= 5/6 kg
Required ratio = 7/6 : 5/6 = 7 : 5
29. In a laboratory, two bottles contain mixture of acid and water in theratio 2 : 5 in the first bottle and 7 : 3 in the second. The ratio in which the
contents of these two bottles be mixed such that the new mixture has acidand water in the ratio 2 : 3 is-
a. 4 : 15
b. 9 : 8
c. 21 : 8
d. 1 : 2
Ans : Quantity of acid in first bottle = 2/7 x mix.
and Quantity of acid in second bottle = 7/10 x mix.
If x and 1 volumes are taken from I and II bottle respectively to form new
mixture.
Then, (2/7 x + 7/10 * 1)/(5x/7 +3/10 * 1) = 2/3
6x/7 21/10 = 10x/7 +6/10
4x/7 = 15/10
x = 15/10*7/4 = 21/8
Required ratio = x : 1
= 21 : 8
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30. A mixture contains 80% acid and rest water. Part of the mixture that
should be removed and replaced by same amount of water to make the ratioof acid and water 4 : 3 is-
a. 1/3 rd
b. 3/7 th
c. 2/3 rd
d. 2/7 th
Ans : Let the initial wt. of mixture be 1 kg and x kg of mixture is taken outand replaced by same amount of water.
Amt. of acid/Amt. of water = 0.8 0.8x/ (0.2 0.2x + x) = 4/3
2.4 2.4x = 0.8 + 3.2x
5.6x = 1.6
x = 1.6/5.6 = 2/7th part
31. An employer reduces the number of his employees in the ratio 9 : 8 and
increases their wages in the ratio 14 : 15. If the original wage bill was Rs.189,900, find the ratio in which the wage bill is decreased-
a. 20 : 21
b. 21 : 20
c. 20 : 19
d. 19 : 21
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Ans : Let the initial number of employees be 9x and the employer gives Rs.
14y as wage to each.
9x * 14y =18900
xy = 150 and The later bill = 8x*15y = 120xy
= 120*150 = 18000
Required ratio = 18000 : 18900
= 20 : 21
32. The batting average for 40 innings of a cricketer is 50 runs. His highest
score exceeds his lowest score by 172 runs. If these two innings areexcluded, the average of the remaining 38 innings is 48 runs. The highestscore of the player is-
a. 165
b. 170
c. 172
d. 174
Ans : Let the max. number of runs be x.
The lowest score = (x-172)
40*50 = 38*48 + x + (x-172)
2000 = 1824 + 2x 172
x= 174
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33. Walking at 3 km per hour, Pintu reaches his school 5 minutes late. If he
walks at 4 km per hour he will be 5 minutes early. The distance of Pintusschool from his house is-
a. 1 Km
b. 2 Km
c. 2 Km
d. 5 Km
Ans : Distance of the school from the house
= 4*3/(4 3) * 5 +5/60 km
= 12*1/6
=2 km
34. Nitin bought some oranges at Rs. 40 a dozen and an equal number atRs.30 a dozen. He sold them at Rs. 45 a dozen and made a profit of Rs.480.The number of oranges, he bought, was-
a. 48 dozen
b. 60 dozen
c. 72 dozen
d. 84 dozen
Ans : Let the number of oranges bought be x.
45x/12 70x/24 = 480
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(45-35)/12 = 480
x = 480*12/10 = 576
= 48*12 = 48 dozen
35. A man buys two chairs for a total cost of Rs.900. By selling one for 4/5of its cost and the other for 5/4 of its cost, he makes a profit of Rs.90 on thewhole transaction. The cost of the lower priced chair is-
a. Rs.360
b. Rs.400
c. Rs.420
d. Rs.300
Ans : Let the cost price of 1 chair be Rs. x.
C.P. of other chair = Rs. (900-x)
4/5 x + 5/4 (900-x) = 900 + 90
4/5 x +1125 -5x/4 = 990
9x/20 = 135
x = 135*20/9
= Rs. 300
C.P. of the lower priced chair is Rs. 300.
36. By selling 100 oranges, a vendor gains the selling price of 20 oranges.His gain per cent is-
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= Rs. 120
Reqd. % profit = (120 100)% = 20%
38. Maninder bought two horses at Rs.40,000 each. He sold one horse at15% gain, but had to sell the second horse at a loss. If he hand suffered a
loss of Rs.3,600 on the whole transaction, then the selling price of thesecond horse is-
a. Rs.30,000
b. Rs.30,200
c. Rs.30,300
d. Rs.30,400
Ans: C.P. of two horses = 2*40000 = Rs. 80000
and S.P. of two horse = 80000 3600 = Rs. 76400
S.P. of the other horse = 76400 46000 = 30400
39. A fruit-seller buys x guavas for Rs.y and sells y guavas for Rs. x. If x>y,then he made-
a. x2 y2 / xy % loss
b. x2 y2 / xy % gain
c. x2 y2 / y2 % loss
d. x2 y2 / y2 * 100% gain
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Ans : C.P. of 1 guava = Rs. y/x [x>y]
and S.P. of 1 guava = Rs. x/y
Reqd. Gain% = x/y y/x/ y/x * 100%
= x2 - y2 /y2 *100%
40. A jar contain 10 red marbles and 30 green ones. How many red marbles
must be added to the jar so that 60% of the marbles will be red?
a. 25
b. 30
c. 35
d. 40
Ans : Let after adding x red marbles, the red marbles with be 60% of the
total.
(10+x)/ (10 + x) + 30 = 60/100
10 + x/40 + x = 3/5
50 + 5x = 120 + 3x
x = 70/2 = 35
41. If a number multiplied by 25% of itself gives a number which is 200%more than the number, then the number is
a. 12
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b. 16
c. 35
d. 24
Ans : Let the number be x.
x*25x/100 = x + 200x/100
x2/4 = 3x
x2 - 12x = 0
x 12 = 0
x = 12
42. The value of an article depreciates every year at the rate of 10% of its
value. If the present value of the article is Rs.729, then its worth 3 yearsago was-
a. Rs.1250
b. Rs.1000
c. Rs.1125
d. Rs.1200
Ans : Let the worth 3 years ago be Rs. x.
729 = x (1 10/100)3
729 = x*9*9*9/10*10*10
x = Rs. 1000
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43. The price of onions has been increased by 50%. In order to keep the
expenditure on onions the same the percentage of reduction in consumptionhas to be-
a. 50%
b. 33 1/3%
c. 33%
d. 30%
Ans : Reqd. Percentage of reduction
= 50*100/(100 + 50) %
= 5000/150 %
= 33 1/3%
44. A took two loans altogether of Rs.1200 from B and C. B claimed 14%simple interest per annum, while C claimed 15% per annum. The totalinterest paid by A in one year was Rs.172. Then, A borrowed-
a. Rs.800 from C
b. Rs.625 from C
c. Rs.400 from B
d. Rs.800 from B
Ans : If A borrowed Rs. x from B. and A borrowed Rs. Rs. (1200 x) from C.
(1200 x)*15*1/100 + x*14*1/100
18000 15x + 14x = 172*100
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x = Rs. 800
45. If a regular polygon has each of its angles equal to 3/5 times of two
right angles, then the number of side is-
a. 3
b. 5
c. 6
d. 8
Ans : If the number of sides a regular polygon be n.
Then (2n-4)/n = 2*3/5
(2n 4)*5 = 6n
n = 5
46. A square is of area 200 sq. m. A new square is formed in such a way
that the length of its diagonal is 2 times of the diagonal of the givensquare. The the area of the new square formed is-
a. 2002 sq.m
b. 4002 sq.m
c. 400 sq.m
d. 800 sq.m
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Ans : Length of the diagonal of Ist square
= 2*200
= 20 m
Length of the diagonal of new square = 202m
Area of the new square = *(20.2)2 = 400 sq. m
47. The heights of a cone, cylinder and hemisphere are equal. If their radiiare in the ratio 2 : 3 : 1, then the ratio of their volumes is-
a. 2 : 9 : 2
b. 4 : 9 : 1
c. 4 : 27 : 2
d. 2 : 3 : 1
Ans : Ratio of their volumes [cone : cylinder : hemisphere]
= 1/3(2)2h : (3)2*h : 2/3(1)2.h
= 4/3 : 9 : 2/3 = 4 : 27 : 2
48. A motor-boat can travel at 10 km/hr in still water. It travelled 91 km
downstream in a river and then returned to the same place, taking
altogether 2 hours. Find the rate of flow of river-
a. 3 km/hr
b. 4 km/hr
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c. 2 km/hr
d. 5 km/hr
Ans : Let the rate of flow of river be x km/hr.
91/(10 + x) + 91/(10 x) = 20
91(10 x + 10 + x)(10 + x) (10 x) = 20
91*20 = 20(100 x2)
x2 = 9 = (3)2
x = 3 km/hr
49. A man driving at 3/4th of his original speed reaches his destination 20
minutes later than the usual time. Then the usual time is-
a. 45 minutes
b. 60 minutes
c. 75 minutes
d. 120 minutes
Ans : Let the original speed be x km/hr and the usual time be y hours.
x * y = x(y+1/3)
4y = 3y + 1
y = 1 hr = 60 minutes
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50. A motor-boat, travelling at the same speed, can cover 25 km upstream
and 39 km downstream in 8 hours. At the same speed, it can travel 35 kmupstream and 52 km downstream in 11 hours. The speed of the stream is
a. 2 km/hr
b. 3 km/hr
c. 4 km/hr