Download - Blue Lotus
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Blue Lotus
Aptitude - TCS
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Problems on Numbers
A car is filled with 4 ¼ gallons of oil for full round trip.
Fuel is taken 1/4 gallon more while going down than
coming up. What is the fuel consumed in coming up?
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Problems on Numbers
Let ‘X’ be the quantity of fuel consumed for the trip in one direction
The fuel consumed while going = X + ¼
The fuel consumed while coming = X
Therefore, the fuel consumed for the trip = (X + ¼) + X = 4 ½
2X + ¼ = 4 ½ => 2X = 4 ½ - ¼ => 2X = 4 ¼ => X= 2 gallons approx
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Problems on Numbers
A box of 150 packets consists of 1kg packets and 2kg
packets. Total weight of box is 264kg. How many 2kg
packets are there?
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Problem on Numbers
114
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Problem on Numbers
The cost of 1 pencil, 2 pens and 4 erasers is Rs.
22, while the cost of five pencils, four pens and
two eraser is 32. how much will 3 pencils, 3
pens and 3 eraser? (TCS)
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Problem on NumbersSolution:
Let Pencil be x, Pens be y, Erasers be z
x + 2y + 4z = 22
5x + 4y + 2z = 32
Adding we get 6x+6y+6z = 54
3x + 3y + 3z = 27
3 Pencil, 3 Pens and 3 Eraser is Rs. 27.
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Problem on Numbers
If the numerator of a fraction is increased by
25% and denominator decrease by 20%, the
new value is 5/4. what is the original value?
(TCS)
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Problem on Numbers
Solution:
( x + 25x/100) / (y – 20y/100) = 5/4
125x / 80y = 5/4
x/y = 5/4 * 80/ 125 = 4/5
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Puzzle
In 80 coins one coin is counterfiet. What is the
minimum number of weighings to find out
counterfiet coin?
(TCS)
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Puzzle
SIX
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Puzzle
In a well of 20feet depth, a frog jumps 5feet up in
the morning and comes 4feet down in the
evening,on which day the frog gets out of the
well.
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Puzzle
Sixteen
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Number System
The number 362 in decimal system is given by
(1362)x in the X system of numbers. find the
value of X.
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Number System
In which of the system, decimal number 184 is
equal to 1234?
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Number System
5
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Number System
Find the value of the 678 to the base 7.
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Number System
1656
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Number System
The base 5 representation of the decimal number 2048
is _____.
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Odd Man Out
a)LINUX b) WINDOWS 98 c)SOLARIS d) SMTP
a)JAVA b) LISP c) Smaltalk d) Eiffle
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Odd Man Out
1.HTTP 2.ARP 3.SNMP 4.SAP
1.Linux 2.windows NT 3.sql server 4.Unix
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Problems on Ages
Father’s age is 5 times his son's age.4 years back
the father was 9 times older than his son. Find
the father's present age? (TCS)
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Problems on Ages
Solution: F = 5SF – 4 = 9(S-4)F – 5s = 0F – 9S = -36 + 4 = -32 4S = 32S = 8Father age = 40 years
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Problems on Ages
One year ago Pandit was three times his sister’s
age. Next year he will be only twice her age.
How old will Pandit be after five years?
(TCS)
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Problems on Ages
Solution:(P-1) = 3(S -1)P + 1 = 2( s+1)P – 3S = -3 + 2 = -2P – 2S = 2-1 = 1S = 3P – 3(3) = -2P – 9 = -2P = -2 + 9 = 7After 5 years = 12
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Problems on Ages
A father is three times as old as his son after 15
years the father will be twice as old as his son’s
age at that time. What is the father’s present
age ? (TCS)
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Problems on Ages
Solution:
F = 3S
F + 15 = 2(S +15)
Father’s age = 45, Son’s age = 15
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•(Quantity of cheaper / Quantity of costlier)
(C.P. of costlier) – (Mean price)
= --------------------------------------
(Mean price) – (C.P. of cheaper)
Alligation or Mixture
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Alligation or Mixture
Cost of Cheaper Cost of costlier c d
Cost of Mixture m
d-m m-c
(Cheaper quantity) : (Costlier quantity) = (d – m) : (m – c)
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A merchant has 100 kg of salt, part of which he sells at 7% profit and the rest at 17% profit. He gains 10% on the whole. Find the quantity sold at 17% profit?
Alligation or Mixture
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Solution: 7 17 10 (17-10) (10-7) 7 : 3The ratio is 7:3The quantity of 2nd kind = 3/10 of 100kg = 30kg
Alligation or Mixture
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A 3-gallon mixture contains one part of S and two
parts of R. In order to change it to mixture containing
25% S how much R should be added?
(TCS)
Alligation or Mixture
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Answer:
R : S2 : 175% : 25%3 : 1
1 gallon of R should be added.
Alligation or Mixture
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In two varieties of tea, one costing Rs. 25/kg.
and the other costing RS. 30/kg are blended to
produce blended variety of tea in ratio 2:3. find
the cost price of the mixture ?
Alligation or Mixture
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Solution: 25 30 x
(30- 28) (28-25) 2 : 3 Let mixed price be xIf you subtract 28 from 30 you will get 2 and if you subtract 25 from 28 you will get 3.
Alligation or Mixture
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Chain Rule
Direct Proportion :
A B
A B
Indirect Proportion:
A B
A B
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Chain Rule
A can copy 50 papers in 10 hours while both A & B can copy 70 papers in 10 hours. Then how many hours are required for B to copy 26 papers?
(TCS)
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Chain Rule
A stationary engine has enough fuel to run 12
hours when its tank is 4/5 full. How long will it
run when the tank is 1/3 full?
TCS Question
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Chain Rule
Answer:
Tank hours
4/5 12
1/3 x
4/5 x = 12 * 1/3
It will run for 5 hours
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Types:
• A invested Rs.x and B invested Rs.y then
A:B = x : y
• A invested Rs. x and after 3 months B invested
Rs. y then the share is
• A:B = x * 12 : y * 9
Partnership
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A sum of money is divided among A, B, C such
that for each rupee A gets, B gets 65 paise and c
gets 35 paise if c’s share is Rs. 560. what is the
sum?
TCS
Share
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Solution
A : B : C
100 : 65 : 35
20 : 13 : 7 Total = 20+13+7 = 40
C’ share = 560
7/40 *X =560
X= 3200
Partnership
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Share
If Rs. 1260 is divided among A, B, C in the
ratio 2 : 3 : 4 what is C’s share?
TCS
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Ratio and Proportion
Solution:
C’s Share = 4/9*1260
C’s share = Rs. 560
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• If A can do a piece of work in n days,
• then A’s 1 day’s work = 1/n
• If A is thrice as B, then:
Ratio of work done by A and B = 3:1
Time and Work
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Pipes and Cisterns
• P1 fills in x hrs. Then part filled in 1 hr is 1/x
• P2 empties in y hrs. Then part emptied in 1 hr
is 1/y
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• P1 and P2 both working simultaneously which fills in x
hrs and empties in y hrs resp ( y>x) then net part filled is 1/x – 1/y
• P1 can fill a tank in X hours and P2 can empty the full
tank in y hours( where x>y), then on opening both pipes, the net part empties in hour 1/y -1/x
Pipes and Cisterns
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One fast typist types same matter in 2 hours and
another slow typist types the same matter in 3
hours. If both do combine in how much time will
they finish?
TCS Question
Time and Work
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Solution:
Fast typist = 1/2 ; slow typist = 1/3 ;
Together:
= 1/2 + 1/3 = 5/6 so 6/5 hrs
The work will be completed in 6/5 Hrs.
Time and Work
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A and B can finish a piece of work in 30 days, B and C
in 40 days, while C and A in 60 days .In how many days
A, B and C together can finish the work ?
Time and Work
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Solution:A + B = 30 days = 1/30B + C = 40 days = 1/40C +A = 60 days = 1/60All work together A+B+C+B+C+A = 1/30 +1/40 +1/602(A+B+C) = 1/30+1/40+1/60 = (4+3+2) /120 = 9/120*2 = 9/240 = 3/80 = 26 2/3 A, B and C can finish the work in 26 2/3 days
Time and Work
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10 men can complete a piece of work in 15 days
and 15 women can complete the same work in 12
days. If all the 10 men and 15 women work
together, In how many days will the work get
completed ?
Time and Work
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Solution:10 men = 15 days means 1day work = 1/1515 men = 12 days means 1 day work = 1/1210 men + 15 women = 1/15 + 1/12 = 4+5/60 = 9/60 = 3/20 20/3 days = 6 2/3 days
The work will be completed in 6 2/3 days.
Time and Work
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Time and Work
A work done by two people in 24 minutes. One
of them can do this work alone in 40 minutes.
How much time is required to do the same work
by the second person?
TCS Question
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Time and Work
Solution :
A and B together = 1/24; A = 1/40; B = ?
= 1/24 – 1/40 = 2/120
= 1/60
The second person will complete in 60 minutes.
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A cistern has two taps which fill it in 12 minutes
and 15 minutes respectively. There is also a
waste pipe in the cistern. When all the pipes are
opened, the empty cistern is filled in 20 minutes.
How long will a waste pipe take to empty a full
cistern ?
Time and Work (Pipes)
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Solution:This problem is based on 2nd method.All the tap work together = 1/12 + 1/15 - 1/20 = 5/60 + 4/60 – 3/60 = 6/60 = 1/10 The waste pipe can empty the cistern in 10
minutes.
Time and Work (Pipes)
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A tap can fill a cistern in 8 hours and another
can empty it in 16 hours. If both the taps are
opened simultaneously, Find the time ( in
hours) to fill the cistern
Time and Work (Pipes)
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Solution:
Tap 1 = 1/8 (fill); Tap 2 = 1/16 (empty)
= 1/8 – 1/16
= 1 / 16
Total time taken to fill the cistern = 16 hours
Time and Work (Pipes)
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Time and Work (Pipes)
A water tank is 2/5th full. Pipe A can fill the tank
in 10 minutes and the pipe B can empty it in 6
minutes. If both the pipes are open, how long
will it take to empty or fill the tank completely?
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Time and Work (Pipes)
Answer :A = 1/10; B = 1/6 = 1/10 -1/6 = - 1/15Empty in 15 minutesTo empty 2/5 of the tank 2/5 * 15 = 6 Time taken (empty)= 6 minutes
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Area and Volume
Cube:
• Let each edge of the cube be of length a. then,
• Volume = a3cubic units
• Surface area= 6a2 sq.units.
• Diagonal = √3 a units.
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Cylinder:
• Let each of base = r and height ( or length) = h.
• Volume = πr2h
• Surface area = 2 πr h sq. units
• Total Surface Area = 2 πr ( h+ r) units.
Area and Volume
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Cone:
• Let radius of base = r and height=h, then
• Slant height, l = √h2 +r2 units
• Volume = 1/3 πr2h cubic units
• Curved surface area = πrl sq.units
• Total surface area = πr (l +r)
Area and Volume
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Sphere:
• Let the radius of the sphere be r. then,
• Volume = 4/3 πr3
• Surface area = 4 π r2sq.units
Area and Volume
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Circle: A= π r 2
Circumference = 2 π r
Square: A= a 2
Perimeter = 4a
Rectangle: A= l x b
Perimeter= 2( l + b)
Area and Volume
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Triangle:
A = ½*base*height
Equilateral = √3/4*(side)2
Area of the Scalene Triangle
S = (a+b+c)/ 2
A = √ s*(s-a) * (s-b)* (s-c)
Area and Volume
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One rectangular plate with length 8inches,breadth 11
inches and 2 inches thickness is there. What is the length of
the circular rod with diameter 8 inches and equal to volume
of rectangular plate?
Area and Volume
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Area and Volume
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If the length of a rectangle is increased by 30% and
the width is decreased by 20%, then the area is
increased by what Percentage?
Area and Volume
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4%
Area and Volume
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The length of a rectangle is increased by 60%. By
what % would the width have to be decreased to
maintain the same area?
Area and Volume
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37.5%
Area and Volume
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• Probability:
P(E) = n(E) / n(S)
• Addition theorem on probability:
n(AUB) = n(A) + n(B) - n(AB)
• Mutually Exclusive:
P(AUB) = P(A) + P(B)
• Independent Events:
P(AB) = P(A) * P(B)
Probability
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There are 19 red balls and One black ball. Ten balls are placed in one jar and remaining in one jar. What is probability of getting black ball in right jar ?
(Infosys -2008)
Probability
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Answer:
Probability is 1/2.
Probability
![Page 77: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/77.jpg)
There are 5 red shoes 4 green shoes. If one
draws randomly a shoe what is the probability of
getting a red shoe?
CTS Question
Probability
![Page 78: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/78.jpg)
Answer:
The probability is 5/9
Probability
![Page 79: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/79.jpg)
A bag contains 2 red, 3 green and 2 blue balls
are to be drawn randomly. Two balls are drawn
at random. What is the probability that the balls
drawn contain only blue balls ?
Probability
![Page 80: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/80.jpg)
Answer :
The probability is 1/21
Probability
![Page 81: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/81.jpg)
Probability
Sam and Jessica are invited to a dance party. If
there are 7 men and 7 women in total at the dance
and 1 woman and 1 man are chosen to lead the
dance, what is the probability that Sam and Jessica
will not chosen to lead the dance ?
![Page 82: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/82.jpg)
Probability
Answer:
The Probability of Selecting = 1/7*7 =
1/49
The Probability of not Selecting = 1-1/49
= 48/49
![Page 83: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/83.jpg)
Probability
The letters of the word SOCIETY are placed
in a row. What is the probability that the three
vowels come together?
![Page 84: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/84.jpg)
Probability
Answer:
Required Probability = (5!*3! )/7!
= 1/7
![Page 85: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/85.jpg)
Average
• Average is a simple way of representing an
entire group in a single value.
• “Average” of a group is defined as:
X = (Sum of items) / (No of items)
![Page 86: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/86.jpg)
Average
Gavaskar’s average in first 50 innings was 50. After the 51st innings his average was 51. How many runs did he make in the 51st innings?
![Page 87: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/87.jpg)
Average
Hansie made the following amounts in seven games of cricket in India: Rs.10, Rs.15, Rs.21, Rs.12, Rs.18, Rs.19 and Rs.17 (all figures in crores).
Find his average earnings.
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Average
Average of 5 number is -10 and sum of 3 numbers is 16.
What is the average of other two numbers?
![Page 89: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/89.jpg)
Average
Average of 5 number is -10 and sum of 3 numbers is 16.
What is the average of other two numbers?
![Page 90: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/90.jpg)
Permutations and Combinations
• Factorial Notation: n! = n(n-1)(n-2)….3.2.1 • Number of Permutations: n!/(n-r)!
• Combinations: n!/r!(n –r)!
![Page 91: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/91.jpg)
A foot race will be held on Saturday. How many
different arrangements of medal winners are
possible if medals will be for first, second and
third place, if there are 10 runners in the race …
Permutations and Combinations
![Page 92: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/92.jpg)
Solution:
n = 10
r = 3
n P r = n!/(n-r)!
= 10! / (10-3)!
= 10! / 7!
= 8*9*10
= 720
Number of ways is 720.
Permutations and Combinations
![Page 93: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/93.jpg)
To fill a number of vacancies, an Employer must
hire 3 programmers from 6 applicants, and two
managers from 4 applicants. What is total
number of ways in which she can make her
selection ?
Permutations and Combinations
![Page 94: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/94.jpg)
Solution:
It is selection so use combination formula
Programmers and managers = 6C3 * 4C2
= 20 * 6 = 120
Total number of ways = 120 ways.
Permutations and Combinations
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In how many ways can the letters of the word
BALLOON be arranged so that two Ls do not
come together?
Permutations and Combinations
![Page 96: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/96.jpg)
Solution:
Total arrangement = 7! / 2!*2! (L and O occurred twice) =1260Ls come together (BAOON) (LL) = 6! / 2! = 3* 4* 5*6* = 360Ls not come together1260 – 360 = 900Number of ways = 900.
Permutations and Combinations
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Permutations and Combinations
A man has 7 friends. In how many ways can
he invite one or more of them to a party?
![Page 98: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/98.jpg)
Permutations and Combinations
Solution:
In this problem, the person is going to select his friends for party, he can select one or more person, so
= 7C1 + 7C2+7C3 +7C4 +7C5 +7C6 +7C7
= 127
Number of ways is 127
![Page 99: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/99.jpg)
Percentage
• By a certain Percent, we mean that many
hundredths.
• Thus, x Percent means x hundredths, written
as x%
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Percentage
After having spent 35% of the money on
machinery, 40% on raw material, 10% on staff,
a person is left with Rs.60,000. What is the total
amount of money spent on machinery and the
raw materials?
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Percentage
Solution:Let total salary =100%Spending:Machinery + Raw material + staff = 35%+40%+10% = 85%Remaining percentage = 100 %– 85% = 15%15 % of X = 60000X = 4, 00,000In this 4, 00,000 75% for machinery and raw material = 4, 00,000* 75/100 = 3, 00,000
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Percentage
If the number is 20% more than the other, how much percent is the second number less
than the first?
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Percentage
Solution:
Let X =20
= X / (100+X) *100%
= 20 /120 *100%
=16 2/3%
The percentage is 16 2/3%
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Percentage
Find the percentage increase in the area of a Rectangle whose length is increased by 20% and breadth is increased by 10%
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Percentage
Answer:
Percentage of Area Change=( X +Y+ XY/100)%
=20+10+20*10/100
=32%
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Percentage
If A’s income is 40% less than B’s income, then how much percent is B’s income more than A’s income?
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Percentage
Answer:
Percentage = R*100%/(100-R) = (40*100)/ (100-40)
=66 2/3%
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Percentage
One side of a square is increased by 30%. To maintain the same area by how much percentage the other side will have to be decreased?
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Percentage
Answer:
Percentage = r*100%/(100+r)
= (30*100) / 130
= 23 1/3%
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Boats and streams
•Up stream – against the stream
•Down stream – along the stream
•u = speed of the boat in still water
•v = speed of stream
•Down stream speed (a)= u+v km / hr
•Up stream speed (b)=u-v km / hr
•u = ½(a+b) km/hr
•V = ½(a-b) km / hr
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A man can row Upstream at 12 kmph and
Downstream at 16 kmph. Find the man’s rate in
still water and rate of the current?
Boats and streams
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Solution:
Rate in still water = 1/2 (16 + 12) = 14 Kmph
Rate of Current = 1/2 (16 – 12 ) = 2 Kmph
Boats and streams
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A Boat is rowed down a river 40 km in 5 hr and
up a river 21 km in 7 hr. Find the speed of the
boat and the river?
Boats and streams
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Solution:
Speed of the Boat Downstream = 40/7 = 8 (a)
Speed of the Boat Upstream = 21/7 = 3 (b)
Speed of the Boat = 1/2 ( a + b ) = 1/2 ( 8+3 )
= 5.5 Kmph
Speed of the River = 1/2 ( a – b ) = 1/2 (8 – 3)
= 2.5 kmph
Boats and streams
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A boat’s crew rowed down a stream from A to B
and up again in 7 ½ hours. If the stream flows at
3km/hr and speed of boat in still water is 5
km/hr. find the distance from A to B ?
Boats and streams
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Solution: Down Stream = Sp. of the boat + Sp. of the stream = 5 +3 =8Up Stream = Sp. of the boat – Sp. of the stream = 5-3 = 2Let distance be XDistance/Speed = Time X/8 + X/2 = 7 ½ X/8 +4X/8 = 15/2 5X / 8 = 15/2 5X = 15/2 * 8 5X = 60 X =12
Boats and streams
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Boats and Streams
A boat goes 40 km upstream in 8 hours and 36 km downstream in 6 hours. Find the speed of the boat in still water in km/hr?
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Boats and Streams
Solution:
Speed of the boat in upstream = 40/8 = 5 km/hr
Speed of the boat in downstream= 36/6 =6 km/hr
Speed of the boat in still water = (5+6 ) / 2
= 5.5 km/hr
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Boats and Streams
A man rows to place 48 km distant and back in 14 hours. He finds that he can row 4 kmph with the stream in the same time as 3 Kmph against the stream. Find the rate of the stream?
![Page 120: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/120.jpg)
Boats and Streams
Solution:Down stream 4 km in x hours. Then,Speed Downstream = 4/x km/hr, Speed Upstream = 3/x km/hr48/ (4/x) + 48/(3/x) = 14x = 1/2Speed of Downstream = 8,Speed of upstream = 6Rate of the stream =1/2 (8-6) km/hr = 1 km/hr
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Time and Distance
•Speed:-
• Distance covered per unit time is
called speed.
Speed = distance/time (or)
•Distance = speed*time (or)
•Time = distance/speed
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• Distance covered α Time (direct variation).
• Distance covered α speed (direct variation).
• Time α 1/speed (inverse variation).
Time and Distance
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• Speed from km/hr to m/sec - (Multi by 5/18).
• Speed from m/sec to km/h, - (Multi by 18/5).
• Average Speed:-
Average speed = Total distance traveled Total time taken
Time and Distance
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From height of 8 m a ball fell down and each
time it bounces half the distance back. What
will be the distance traveled?
Sathyam Question
Time and Distance
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Solution:
= 8 + 4 + 4+2+2+1+1+0.5+0.5 +….etc.
The total distance traveled is 24 m
Time and Distance
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Two cars are 15 km apart. One is running at a
speed of 50 kmph and the other at 40 kmph. How
much time will it take for the two cars to meet?
Sathyam Question
Time and Distance
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Solution:
Time taken
=Distance / (S1 – S2)
= 15 / (50 – 40)
= 15 / 10
= 1.5
It will take 1½ hours.
Time and Distance
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The center of a storm shifts 22.5 miles in 1 hour. At
the same rate what time will it take to move 60
miles?
TCS Question
Time and Distance
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Answer:
For 22.5 miles it takes 1 hour
It means for 60 miles T = D / S
Time taken = 60 / 22.5
It will take 2 2/3 hours.
Time and Distance
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Time and Distance
By walking at ¾ of his usual speed, a man
reaches office 20 minutes later than usual.
Find his usual time?
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Time and Distance
Solution:
Usual time = Numerator * late time
= 3*20
= 60
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Time and Distance
A man on motorcycle rides 110 miles in 330 minutes. What is his average speed in miles per hour?
TCS Question
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Time and Distance
Answer:
Speed = D / T =110*60 /330
The average speed = 20 miles/hour
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Time and Distance (Trains)
A train starts from Delhi to Madurai and at the
same time another train starts from Madurai to
Delhi after passing each other they complete
their journeys in 9 and 16 hours, respectively.
At what speed does second train travels if first
train travels at 160 km/hr ?
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Time and Distance (Trains)
Solution:
Let x be the speed of the second train
S1 / S2 = √T2/T1
160/x = √16/9
160/x = 4/3
x = 120
The speed of second train is 120km/hr.
![Page 136: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/136.jpg)
Time and Distance (Trains)
Two hours after a freight train leaves Delhi a
passenger train leaves the same station traveling in
the same direction at an average speed of 16 km/hr.
After traveling 4 hours the passenger train overtakes
the freight train. What was the average speed of the
freight train? Wipro Question
![Page 137: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/137.jpg)
Time and Distance (Trains)
Solution :
Speed of Passenger train = 16 kmph
Distance = 16*4 = 64
Speed of freight train = Distance / ( S1 + S2 )
= 64 / (4+2)
= 64/6
= 10.6 km/hr
The average speed = 10.6 km/hr
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Time and Distance (Trains)
There are 20 poles with a constant distance
between each pole. A train takes 24 sec to
reach the 12 pole. How much time will it take
to reach the last pole ?
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Time and Distance (Trains)
Solution:
To cross 11 poles it is taking 24 sec
To cross 19 poles it will take x time
Poles time
11 24
19 x
11x = 19 * 24
x = 19* 24 /11
x = 41.45 sec
It reaches the last pole in 41.45sec
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Time and Distance (Trains)
120 m long train crosses the pole after
2½ sec. Find how much time it takes to cross
140 m long platform?
Caritor Question
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Time and Distance (Trains)
Solution:
To cross 120 m it is taking 2 ½ sec. (5/2sec)
To cross (120 +140)=260 m it will take x sec
120x = 260*5/2 (apply chain rule)
= 5 5/12
It takes 5 5/12 seconds.
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Time and Distance (Trains)
A train X speeding with 120 kmph crossed another train Y, running in the same direction, in 2 minutes. If the lengths of the trains X and Y be 100 m and 200m respectively, what is the speed of train Y?
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Time and Distance (Trains)
Solution:Let the speed of train Y be x km/hrRelative Speed of X to Y = (120 –x) km/hr = [(120 –x)*5/18] m/sec =( 600 – 5x) / 18 m/secT = D / Rel. Speed300 / (600 – 5x /18) = 120 ( 2 Minutes ) 5400 = 120 (600 -5x) x = 111 m/sec.
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CalendarOdd days:
0 = Sunday
1 = Monday
2 = Tuesday
3 = Wednesday
4 = Thursday
5 = Friday
6 = Saturday
![Page 145: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/145.jpg)
CalendarMonth code: Ordinary year
J = 0 F = 3
M = 3 A = 6
M = 1 J = 4
J = 6 A = 2
S = 5 O = 0
N = 3 D = 5
Month code for leap year after Feb. add 1.
![Page 146: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/146.jpg)
Calendar
Ordinary year = (A + B + C + D )-2
-----------------------take remainder
7
Leap year = (A + B + C + D) – 3
------------------------- take remainder
7
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What is the day of the week on 30/09/2007?
Calendar
![Page 148: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/148.jpg)
Solution:
A = 2007 / 7 = 5
B = 2007 / 4 = 501 / 7 = 4
C = 30 / 7 = 2
D = 5
( A + B + C + D )-2
= -----------------------
7
= ( 5 + 4 + 2 + 5) -2
----------------------- = 14/7 = 0 = Sunday
7
Calendar
![Page 149: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/149.jpg)
What was the day of the week on 13th May,
1984?
Calendar
![Page 150: Blue Lotus](https://reader035.vdocument.in/reader035/viewer/2022062308/56814c4e550346895db95a23/html5/thumbnails/150.jpg)
Clock:
•In every Hour, the minute hand gains 55 minutes on the hour hand
•In every hour both the hands coincide once. = (11m/2) – 30h (hour hand to min hand)
= 30h – (11m/2) (min hand to hour hand)
•If you get answer in minus, you have to subtract your
answer with 360 o
Clocks
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Clocks
Find the angle between the minute hand and
hour hand of a clock when the time is 7:20.
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Solution:
= 30h – (11m/2)
= 30 (7) – 11 20/2
= 210 – 110
= 100
Angle between 7: 20 is 100o
Clocks
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Clocks
At what time between 7 and 8 o’clock will the
hands of a clock be in the same straight line but,
not together?
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Clocks
Solution: h = 7
= 30h – 11m/2
180 = 30 * 7 – 11 m/2
On simplifying we get ,
5 5/11 min past 7
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In interpretation of data, a chart or a graph is
given. Some questions are given below this chart
or graph with some probable answers. The
candidate has to choose the correct answer from
the given probable answers.
Data Interpretation
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• 1. The following table gives the distribution of students according to
professional courses:
__________________________________________________________________
Courses Faculty
___________________________________
Commerce Science Total
Boys girls Boys girls
___________________________________________________________
• Part time management 30 10 50 10 100
• C. A. only 150 8 16 6 180
• Costing only 90 10 37 3 140
• C. A. and Costing 70 2 7 1 80
__________________________________________________________________
• On the basis of the above table, answer the following questions:
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The percentage of all science students over
Commerce students in all courses is
approximately:
(a) 20.5 (b) 49.4
(c) 61.3 (d) 35.1
Data Interpretation
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Answer:
Percentage of science students over commerce
students in all courses = 35.1%
Data Interpretation
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What is the average number of girls in all
courses ?
(a) 15 (b) 12.5
(c) 16 (d) 11
Data Interpretation
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Answer:
Average number of girls in all courses = 50 / 4
= 12.5
Data Interpretation
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What is the percentage of boys in all courses
over the total students?
(a) 90 (b) 80
(c) 70 (d) 76
Data Interpretation
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Answer:
Percentage of boys over all students
= (450 x 100) / 500
= 90%
Data Interpretation
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Venn Diagram
If X and Y are two sets such that X u Y has 18
elements, X has 8 elements, and Y has 15
elements, how many element does X n Y have?
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Venn Diagram
Solution:
We are given n (X uY) = 18, n (X) = 8, n (Y) =15. using the formula.
n( X n Y) = n (X) + n (Y) - n ( X u Y)
n( X n Y) = 8 + 15 – 18
n( X n Y) = 5
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Venn Diagram
If S and T are two sets such that S has
21elemnets, T has 32 elements, and S n T has
11 elements, how many element elements does
S u T have?
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Venn Diagram
Answer:
n (s) = 21, n (T) = 32, n ( S n T) = 11,
n (S u T) = ?
n (S u T) = n (S) + n( T) – n (S n T)
= 21 + 32 – 11 = 42
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Venn Diagram
If A and B are two sets such that A has 40
elements, A u B has 60 elements and A n B
has 10 elements, how many element elements
does B have?
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Venn Diagram
Answer:
n ( A) = 40, n ( n B) = 60 and n ( A n B) = 10,
n ( A u B) = n ( A) + n (B) – n ( A n B)
60 = 40 + n (B) – 10
n (B) = 30
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Venn Diagram
In a group of 1000 people, there are 750 people
who can speak Hindi and 400 who can speak
English. How many can Speak Hindi only?
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Answer:
n( H u E) = 1000, n (H) = 750, n (E) = 400,
n( H u E) = n (H) + n (E) – n( H n E)
1000 = 750 +400 – n ( H n E)
n ( H n E) = 1150 – 100 = 150
No. of people can speak Hindi only
_
= n ( H n E) = n ( H) – n( H n E)
= 750 – 150 = 600
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Venn Diagram
In a class of 100 students, the number of students passed in English only is 46, in maths only is 46, in commerce only is 58. the number who passes in English and Maths is 16, Maths and commerce is 24 and English and commerce is 26, and the number who passed in all the subject is 7. find the number of the students who failed in all the subjects.
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Venn Diagram
Solution:
No. of students who passed in one or more subjects
= 11+ 9 + 13 + 17 + 15 + 19 + 7 = 91
No of students who failed in all the subjects
= 100 -91 = 9
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Venn Diagram
In a group of 15, 7 have studied Latin, 8 have
studied Greek, and 3 have not studied either.
How many of these studied both Latin and
Greek?
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Venn Diagram
Answer:
3 of them studied both Latin and Greek.