chain rule.44

Chain Rule1. The price of 357 mangoes is Rs.1517.25. What will be the approximate price

of 49 dozens of such mangoes? Ans Rs.2,500 Difficulty Level : Easy Basic Formula: Direct Proportion Moderately easy Difficult

Answer with Explanation: Let x be the cost of 49 dozens of mangoes 357 : (49 X12) 357X x x = = = = 1517.25 : x49 X 12 X 1517 .25 357

Rs. 2499 Rs.2500 (approximately)

Chain Rule, BU

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2. The price of 438 oranges is Rs.1384.08. What will be the approximate price

of 8 dozen of oranges? ans Rs.300 Difficulty Level : Easy Basic Formula: Direct Proportion Moderately easy Difficult

Answer with Explanation: Let x be 8 dozens of oranges 438 : 8 X 12 438x X X = Rs. 300/= = = 1384.08:x 96 X 1384.0896 X 1384 .08 438

Chain Rule, BU

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3. If 11.25m of uniform iorn rod weights 42.75kg. What will be the weight of

6m of the same rod? Ans Rs.22.8kg Difficulty Level : Easy Basic Formula: Direct Proportion Moderately easy Difficult

Answer with Explanation: Let x be the weight of the rod Length 11.25 6 11.25x X = = Weight 42.75 x 6 X 42.756 X 42 .75 11 .25

Weight of the rod

=

22.8 kg.

Chain Rule, BU

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4. On a scale of a map 0.6 cm represents 6.6km. If the distance between two points on the map is 80.5 cm , the actual distance between these points is Ans:885.5km Difficulty Level : Easy Basic Formula: Direct Proportion Moderately easy Difficult

Answer with Explanation: Scale 0.6 80.5 0.6 X x x x = = = Distance 6.6 x 6.6 X 80.56.6 X 80 .5 0 .6

885.5 km.

Chain Rule, BU

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5. If 20 men working together can finish a job in 20 days, then the numbers of days taken by 25 men of the same capacity to finish the job is ans : 16 Difficulty Level : Easy Basic Formula: Indirect Proportion Moderately easy Difficult

Answer with Explanation: Number of men 20 25 Number of days 20 x

Let x be the number of days taken 25 men 20 X 20 = x x = = 25 X x 400/25 16 days

Chain Rule, BU

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6. If 10 men can reap a field in 8 days, then 8 men will reap the same field in :

ans:10 days Difficulty Level : Easy Basic Formula: Indirect Proportion Moderately easy Difficult

Answer with Explanation: Number of men 10 8 Number of days 8 x

Let x be the number of days taken 8 men 10 X 8 x x = = = 8Xx 80/8 10 days

Chain Rule, BU

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7. 14 pumps of equal capacity can fill a tank in 6 days, if the tank has to be filled in 4 days. The number of extra pumps needed is : Ans 7 Difficulty Level : Easy Basic Formula: Indirect Proportion Moderately easy Difficult

Answer with Explanation: Number of pumps 14 x Let x be the pumps needed 6 X 14 X = 84/4 X = = = 4Xx 21 21 pumps Number of days 6 4

Already there are 14 pumps available

Extra pumps =

21 - 14 = 7

Chain Rule, BU

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8. If 6 men working 7 hours a day can plough a field in 48 days, in how many days will 14 men working 12 hours a day plough the same field ? Ans: 32 Difficulty Level : Easy Basic Formula: Indirect Proportion More men, less days More time, Less days Indirect proportion Indirect proportion Moderately easy Difficult

Answer with Explanation: Step 1 Number of men 10 8 Step 2 6 X7 X 48 = X X = = 14 X 12 X x6 X7 X 48 14 X 12

Number of Hours 7 12

Number of days 8 x

12 days

Chain Rule, BU

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9. If 80 lamps can be lighted 5 hours per day for 10 days for Rs.21.24 then the number of lamps which can be lighted 4 hours daily for 30 days for Rs.76.50 is Ans:120 Difficulty Level : Easy Basic Formula: Less hours, More lamps More days, less lamps More money, more lamps Answer with Explanation: Number of hours 5 4 5 X 10 X 76.50 X 80 x x Days 10 30 = = = Amount 21.24 76.50 4 X 30 X 21.24 X x5 X 10 X 76.50 X 80 4 X 30 X 21.24 X x

Moderately easy

Difficult

-

Indirect proportion Indirect proportion Direct Proportion

Lamps 80 x

120 lamps

Chain Rule, BU

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10.If 12 carpenters, working 6 hours a day can make 460 chairs in 24 days, how many chairs will 18 carpenters make in 36 days, each working 8 hours a day ? Ans: 1380 Difficulty Level : Easy Basic Formula: More carpenters, more chairs More hours, more chairs More days, more chairs Answer with Explanation: Number of carpenters 12 14 hours 6 8 = = = Days 24 36 18 X 8 X 36 X 46018 X 8 X 36 X 460 12 X 6 X 24

Moderately easy

Difficult

-

Direct proportion Direct proportion Direct proportion

chairs 460 x

12 X 6 X 24 X xx x

1380 Chairs

Chain Rule, BU

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11. 400 person working 9 hours per day complete 1/4th of the work in 10 days.

The number of additional persons, working 8 hours per day required to complete the remaining working in 20 days is Ans: 275 Difficulty Level : Easy Basic Formula: Less hours, More men required More days, less men required More work, More men required Indirect Proportion Indirect Proportion Direct Proportion Moderately easy Difficult

Answer with Explanation: Let x be the number of persons completing the work in 20 days Step 1 work done = , Remaining work = 1 = Hours 9 8 Step 2 9 X X 10 X 400 X Already available persons = = = 8 X X 20 X x9 X X 10 X 400 8 X X 20

hours 1/4 3/4

Days 10 20

men 400 x

=

675

400 = 275

Additional persons =

675 400

Chain Rule, BU

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12.Some persons can do a piece of work in 12 days. Two times the number of such persons will do half of that work in Ans : 3 days Difficulty Level : Easy Basic Formula: More men, less days Less work, less days Indirect Proportion Direct Proportion Moderately easy Difficult

Answer with Explanation: Let x be the required number of days and y be the men can do the work in 12 days Men Y 2y Y x 12 x = x = work 1 2y X x X 1 6y/2y = 3 days days 12 X

Chain Rule, BU

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13. If 8 persons can build a will 140m long in 42 days, the number of days that

30 persons will take to complete a similar wall 100 m long is Ans 8 Difficulty Level : Easy Basic Formula: Indirect and Direct proportion Moderately easy Difficult

Answer with Explanation: Let x be the required number of days Men 8 30 Length 140 100 days 42 x Indirect proportion Direct proportion

More men, less days required

Less length, less days required 8 X 100 X 42 x x = = =

30 X 140 X x8 X 100 X 42 30 X 140

8

Chain Rule, BU

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14. If it takes 10 days to dig a trench 100m long, 50m broad and 10m deep. What length of trench, 25m board and 15m deep can be dug in 30 days ? Ans 400m Difficulty Level : Easy Basic Formula: Direct and Indirect Proportions Moderately easy Difficult

Answer with Explanation: Let x be the required length Days 10 30 Breadth 50 25 depth 10 15 = = length 100 x Direct proportion Indirect proportion Indirect proportion

More days, More length More breadth, less length More depth, less length

10 X 25 X 15 X xx

30 X 50 X 10 X 100 400M

Chain Rule, BU

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15.

A certain number of men can finish a piece of work in 100 days. If however there were 10 men less, it would take 10 days more for the work to be finished, how many men were there originally? Ans 110 Difficulty Level : Easy Basic Formula: Indirect Proportion Answer with Explanation: Let x be the number of men originally If there were 10 men less then The number of men = = Number of men x x 10 Less men, More days x X 100 100x X = = = days 100 110 110x 1100 110 Indirect proportion (x 10) X 110 x 10 100 + 10 = 110 days Moderately easy Difficult

The number of days to finish the job by (x 10) men

Chain Rule, BU

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16.

A certain number of men could do a piece of work in 60 days. If there

were 8 more men, it could be finished in 10 days. Less. The number of men in the beginning were Ans:40 Difficulty Level : Easy Basic Formula: Indirect proportion Answer with Explanation: Let x be the number of men originally If 8 more men were added, then The number of men = x + 8 Given the work could be finished in 10 days less Moderately easy Difficult

The number of days =Number of men x x+8 days 60 50

60 10

= 50 days

More men, Less days Indirect proportion x X 60 60x x = = = (x + 8) X 50 50x + 400 40 men

Chain Rule, BU

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17.

If 18 binder bind 900 book sin 10 days. How many binder will be

required to bind 660 books in 12 days Ans 11 Difficulty Level : Easy Basic Formula: Direct and Indirect proportion Moderately easy Difficult

Answer with Explanation: Let x be the number of binders required Books 900 660 days 10 12 Number of Binders 18 x

Less books, less binders More days, less binders

Direct proportion = = Indirect Proportion 660 X 10 X 18 11 Binders

900 X 12 X xx

Chain Rule, BU

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18.

If 300 men can do a piece of work in 16 days, how many men would do

1/5 of the work in 15 days? Ans :64 Difficulty Level : Easy Basic Formula: Direct and Indirect proportion Moderately easy Difficult

Answer with Explanation: Let x be the number of men required to complete 1/5 of the work in 15 days Work 1 1/5 days 16 15 Number of men 300 x

Less work, less men less days, more men

= =

Direct proportion Indirect Proportion 1/5 X 16 X 300 64 men

1 X 15 X xx

Chain Rule, BU

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19.

If 6 men working 8 hours a day earn Rs.840 per week then 9 men

working 6 hours a day will earn how much per week? Ans: 945 Difficulty Level : Easy Basic Formula: Direct Proportion Moderately easy Difficult

Answer with Explanation: Let x be the amount Earned Number of Men 6 9 More men, More amount Less hours, Less amount 6X8Xx x = = Hours 8 6 9 X6 X 840 Rs. 945/Amoutn 840 x Direct Proportion Direct Proportion

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20.

If 17 laborers can dig a ditch 26m long in 18 days, working 8 hours a day

how many more laborers should be engaged to dig a similar ditch 39 m long in 6 days, each labour working 9 hours a day? Ans 51 Difficulty Level : Easy Basic Formula: Direct and Indirect Proportion Answer with Explanation: Let x be the number of labourers required Length 26 39 Days 18 6 hours 8 9 Labourers 17 x Direct Proportion Indirect Proportion Indirect Proportion Moderately easy Difficult

More length, more labourers Less days, more labourers More hours, Less labourers

26 X 6 X 9 X xX X = =

=

39 X 18 X 8 X 17

39 X 18 X 8 X 17 26 X 6 X 9

68 17 68 17 = 51

Number of labourers already availed =

Number of labourers required =

Chain Rule, BU

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21.

If 18 pumps can raise 2170 tones of water in 10 days, working 7 hours a

day in how many days will 16 primps raise 1736 tonnes of water, working 9 hours a day? Ans 7 days Difficulty Level : Easy Basic Formula: Direct and Indirect Proportion Answer with Explanation: Let x be the required number of days Pumps 18 16 Quantity 2170 1736 Hours 7 9 Days 10 x Moderately easy Difficult

Less pumps, More days Less quantity, less days More hours, less days

Indirect proportion direct proportion Indirect proportion

18 X 1736 X 7 X 10 =x x = =

16 X 2170 X 9 X x

18 X 1736 X 7 X 10 16 X 2170 X 9

7 days

Chain Rule, BU

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22.

If 9 examiners can examine a certain number of answer books in 12 days

by working 5 hours a days for how many hours a day would 4 examiners have to work in order to examine twice the number of answer books in 30 days? Ans 9 Difficulty Level : Easy Basic Formula: Direct Proportion and Indirect proportion Answer with Explanation: Let the required number of working hours per day be x. Let the number of answer books be 1. Examiners 9 4 books 1 2 days 12 30 = = = = hours 5 x Indirect proportion Direct Porportion Indirect proportion Moderately easy Difficult

Less examiner, more hours More answer books, more hours More days, less hours 9 X 12 X 2 X 5 x =

4 X 1 X 30 X x

9 X 12 X 2 X 5 4 X 1 X 30

x

=

9 hours per day.

Chain Rule, BU

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23.

A rope makes 70 rounds of the circumference of a cylinder whose radius

of the base is 14cm. how many times can it go round a cylinder with radius 20 cm ? Ans 49 Difficulty Level : Easy Basic Formula: Indirect Proportion Answer with Explanation: Let x be the required number of rounds Radious (cm) 14 20 Number of rounds 70 x Moderately easy Difficult

More radious, less number of rounds Indirect Proportion

14 X 70X =

= =

20 X x 49 rounds

14 X 70 / 20

x

Chain Rule, BU

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24. A, B and C are employed to do a piece of work for Rs.529. A and B together are supposed to do 19/23 of the work and B and C together 8/23 of the work. What amount should A be paid? Rs.315 Rs.375 Difficulty Level : Easy Basic Formula: If A, B and C are doing a combined work and if B and C do together, then As job is given by 1 (B+C)s work Answer with Explanation: Given B and C do the job together = = = = 8 /23 15/23 529 X 15/23 Rs. 345/Moderately easy Difficult Rs.345 Rs.355

As workAs Share

=

1 8/23

Chain Rule, BU

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25. A can lay railway track between given stations in 16 days and B can do the same job in 12 days. With the help of C, they did the job in 4 days only. Then, C alone can do the job in : 9 1/5 days days Difficulty Level : Easy Basic Formula: If A can do a piece of work in n days. Then As 1 days work = 1/n Answer with Explanation: Given (A+B+C)s 1 days work As days work Bs days work = = = = 1/16 1/12 = - (1/16 +1/12) = 5/48 - 7/48 9 3/5 days. Moderately easy Difficult 9 2/5 days 9 3/5 days 10

days work Cs alone can do the work in 48/5 = C

Chain Rule, BU

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26. Ronald and Elan are working on an assignment. Ronald takes 6 hours to type 32 pages on a computer, while Elan takes 5 hours to type 40 pages. How much time will they take, working together on two different computers to type an assignment of 110 pages? 7 hours 30 minutes minutes 8 hours 25 minutes Moderately easy Difficult 8 hours 8 hours 15

Difficulty Level : Easy Basic Formula:

If A can do a job n hours, then As work in 1 hour = 1/n Answer with Explanation: Number of pages typed by Ronald in 1 hour = 32/6 = 16/3 Number of pages typed by Elan in 1 hour = 40/5 = 8 Number of pages typed by both in 1 hour = (16/3 +8) = 40/3

Time taken by both to type 110 pages = (110X 3/40) hours= = 8 hours 8 hours 15 minutes.

Chain Rule, BU

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27. A and B can do a work in 12 days, B and C in 15 days, C and A in 20 days. If A, B and C work together, they will complete the work in: 5 days 15 2/3 days Difficulty Level : Easy Basic Formula: If A and B can do a work in n days Then (A + B)s 1 days work Answer with Explanation: Given (A +B)s 1 days work (B +C)s 1 days work (A +C)s 1 days work = = = 1/12 1/15 1/20 1/12 + 1/15 + 1/20 12/60 = 1/5 X 1/5 = 1/10 = 1/n Moderately easy Difficult 7 5/6 days 10 days

Adding we get, 2 (A+B+C)s 1 days work = =

(A+B+C)s 1 days work

=

A, B and C together can complete the work in 10 days.

Chain Rule, BU

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28. A works twice as fast as B. If B can complete a work in 12 days independently, the number of days in which A and B can together finish the work is: 4 days 18 days Difficulty Level : Easy Basic Formula: If A is twice as good a workman as B The ratio of work done by A and B And ratio of time taken by A and B Answer with Explanation: Ratio of rates of working of A and B = So, ratio of time taken As 1days work Bs 1days work (A+B) s 1days work = = = = 1:2 1/6 1/12 1/6 + 1/12 = 3/12 = 1:2 = = 2:1 1:2 Moderately easy Difficult 6 days 8 days

A and B together can complete the work in 4 days.

Chain Rule, BU

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29. 12 men can complete a piece of work in 4 days, while 15 women can complete the same work in 4 days. 6 men start working on the job and after working for 2 days, all of them stopped working. How many women should be put on the job complete the remaining work, if it is to be completed in 3 days? 15 Difficulty Level : Easy Basic Formula: Man A can do a job in n days Then As 1 days work = 1/n Answer with Explanation: 12 men can complete the work in 4 days 1 mans 1 days work = = = = 1/48 1/60 6/48 X 2 1- = = 15 women can complete the same work in 4 days 18 22 Moderately easy None of these Difficult

1 womans 1 days work6 mens 2 days work Remaining work

Now, 1/60 work is dine in 1 day by 1 woman. So work will be done in 3 days by (60 X X 1/3) = 15 women.

Chain Rule, BU

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30. A and B together can do a piece of work in 30 days. A having worked for 16 days, B finishes the remaining work alone in 44 days. In how many days shall B finish the whole work alone? 30 days Difficulty Level : Easy Basic Formula: A can do a work in n days Then As 1 days work = 1/n Answer with Explanation: Let As 1 days work Bs 1 days work Then x+y = = = = Bs 1 days work = x y 1/30 16x +44y 1/ 60 = 1 y = 1/60 40 days 60 days 70 days Difficult

Moderately easy

Solving above equations, x = 1/60,

B alone can finish the work in 60 days.

Chain Rule, BU

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31. A can do a piece of work in 14 days which B can do in 21 days. They begin together but 3 days before the completion of the work, A leaves off. The total of days to complete the work is: 6 3/5 Difficulty Level : Easy Basic Formula: A can do a work in n days Then As 1 days work = 1/n Answer with Explanation: Bs 3 days work Remaining work (A+B)s 1 days work = = = (1/21 X 3) = 1/7 1 1/7 = 6/7 5/42 1/14 + 1/21 = 8 1/2 Moderately easy 10 1/5 Difficult 13

5/42 work is done by A and B in 1 day

6/7 work is done by A an B in (42/7 X 6/7) = 36/5 daysTotal time taken= = 3 + 36/5 10 1/5 days.

Chain Rule, BU

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32. If 7 spiders make 7 webs in 7 days, then 1 spider will 1 web in how many days? Answer : 7 Difficulty Level : Easy Basic Formula: Direct proportion and indirect proportion Moderately easy Difficult

Answer with Explanation: Let x be the required number of days Number of spiders 7 1 webs 7 1 days 7 x Indirect proportion Direct proportion 1XxX7 = 7 days.

Less spiders, more days Les webs, less days = =

7 X 7 X 1X

7 X 7 X1 1X 7

Chain Rule, BU

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33. 4 mat weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weavers in 8 days? Answer : 16 Difficulty Level : Easy Basic Formula: Direct Proportion Answer with Explanation: Let the required number of mats be x. Number of weavers 4 8 More weavers, more mats More days, More mats mats 4 x = = days 4 8 Direct proportion Direct proportion Moderately easy Difficult

4 X 4 X xX

8X8X4 = 16 mats.

8X8X 4 4X4

Chain Rule, BU

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34. In a camp, there is a meal for 120 men or 200 children. If 150 children have taken the meal, how many men will be catered to with the remaining meal? Answer : 30 Difficulty Level : Easy Basic Formula: Facts on proportion Answer with Explanation: There is a meal for 200 children 150 children have taken the meal Remaining meal is to be catered to 50 children Given 200 children = 120 men Moderately easy Difficult

50 children = (120/200 X 50) men = 30 men Remaining meal will be catered to 30 men.

Chain Rule, BU

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35. 39 persons can repair a road in 12 days, working 5 hours a day. In how many days will 30 persons, working 6 hours a day, complete the work? Answer : 13 Difficulty Level : Easy Basic Formula: Indirect proportion Moderately easy Difficult

Answer with Explanation: Let the required number of hours per day be x Number of persons 39 30 Less persons, more days More hours, less days = = hours / day 5 6 days 12 x

Indirect proportion Indirect proportion 30 X x X 639 X 12 X 5 6 X 30

39 X 12 X 5x days.

=

13

Chain Rule, BU

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36. In a dairy farm, 40 cows eat 40 bags of husk in 40 days. In how many days one cow will eat one bag of husk? Answer : 40 Difficulty Level : Easy Basic Formula: Direct and Indirect proportion Answer with Explanation: Let x be the required number of days. Number of cows 40 1 Less cows, More days Less bags, less days bags 40 1 days 40 x Indirect proportion Direct proportion = = 1 X x X 4040 X 40 X 1 1 X 40

Moderately easy

Difficult

40 X 40 X 1x days.

=

40

Chain Rule, BU

Page 36


37. A fort had provision of food for 150 men for 45 days. After 10 days, 25 men left the fort. The number of days for which the remaining food will last, is : Answer : 42 Difficulty Level : Easy Basic Formula: Indirect Proportion Answer with Explanation: After 10 days, 150 men had food for 35 days. Suppose 125 men had food for x days Less men, more days Number of men 150 125 150 X 35 x x = = = 125 X x 150 X 35 / 125 42 days. Indirect proportion days 35 x Moderately easy Difficult

Chain Rule, BU

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38. A does half as much work as B and C does half as much work as A and B together. If C alone can finish the work in 40 days, then together all will finish the work in : Answer : 13 1/3 Difficulty Level : Easy Basic Formula: Facts on time and work Answer with Explanation: (As 1 days work) : (Bs 1 days work)3x + 2 x 2

Moderately easy

Difficult

=

150 :100

Let As and Bs 1 days work be 3x and 2x respectively Then Cs 1days work = = 5x / 2

5x / 2 = 1/40X = 1x / 40 X 2/5 = 1/100 As 1 days work = Cs 1 days work = 3/100, Bs 1 days work = 1/40 3/100 +1/50+1/40 = 3/40 1/50

(A+B+C)s 1 days work =

A, B and C together can do the work = 40/3 = 13 1/3 days

Chain Rule, BU

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39. The rates of working of A and B are in the ratio 5:6 the number of days taken by them to finish the work are in the ratio : Answer : 6:5 Difficulty Level : Easy Basic Formula: Facts on Time and work Moderately easy Difficult

Answer with Explanation: Ratio of work done by A and B = 5:6 = 6:5

Ratio of time taken by A and B to finish the job

Chain Rule, BU

Page 39


40. 95 men have provision for 200 days. After 5 days, 30 men died due to an epidemic. The remaining food will last for how many days? Answer : 285 Difficulty Level : Easy Basic Formula: Indirect proportion Answer with Explanation: Let the remaining food will last for x days. After 5 days, 95 men had provisions for 195 days and 65 men had provisions for x days. Number of Men 95 65 days 195 x = = = 65 X x 95 X195/ 65 285 days. x Moderately easy Difficult

95 X195 x

Chain Rule, BU

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41. If 21 cows eat that much as 15 buffaloes, how many cows will eat that much as 105 buffaloes? Answer : 147 Difficulty Level : Easy Basic Formula: Direct proportion Answer with Explanation: Let x be the number of cows. Buffaloes 15 105 Cows 21 x Moderately easy Difficult

More buffaloes, More cows Direct Proportion

105 X21x

= = =

15 X x 105 X21/ 15 147 cows.

x

Chain Rule, BU

Page 41


42. Ten pipes through which water flows at the same rate can fill a tank in 28 minutes. If three pipes go out of order, how long will the remaining pipes take to fill the tank? Answer : 40 min Difficulty Level : Easy Basic Formula: Indirect proportion Moderately easy Difficult

Answer with Explanation: Let x be the required minutes There are 10 pipes initially. If three pipes go out or order, then there are 10-3 = 7 pipes Number of Pipes 10 7 Less pipes, More time Time (min) 28 x = = = Direct Proportion 7Xx 10 X28/ 7 280/7 = 40 min.

10 X28x

x

Chain Rule, BU

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43. If 3/5 of a cistern is filled in 1 minute, how much more time will be required to fill the rest of it Answer : 40 sec Difficulty Level : Easy Basic Formula: Direct Proportion Answer with Explanation: Let x be the required time to fill the rest of the cistern 1 -3/5 = 2/5 Portion of the cistern 3/5 2/5 Less protion, Less time Time (sec) 60 x Direct Proportion 60 X 2/560 X 2/5 3/5

Moderately easy

Difficult

3/5 X xx

= = =

x

40 secs.

Chain Rule, BU

Page 43


44. A contractor undertook to do a price of work in 40 days. He engages 100 men at the beginning and 100 more after 35 days and completes the work in stipulated time. If he had not engaged the additional men, how many days behind schedule would it be finished? Answer :5 Difficulty Level : Easy Basic Formula: Facts on Time and work Answer with Explanation: If 100 additional men are added, there are 200 men Moderately easy Difficult

after 35 days, 200 men are working.Then (100 X 35) + (200 X 5) men = 4500 men can finish the job in 1 day.

100 men can finish the job in 4500/100 = 45 40 =5 days

45 days

The work will be completed 5 days behind the schedule.

Chain Rule, BU

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chain rule.44

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