# Chain Rule Questions

FACTS  AND  FORMULAE  FOR  CHAIN  RULE  QUESTIONS

1. Direct Proportion: Two quantities are said to be directly proportional, if on the increase (or decrease) of the one, the other increases (or decreases) to the same extent.

Ex. 1. Cost is directly proportional to the number of articles. (More Articles, More Cost)

Ex. 2. Work done is directly proportional to the number of men working on it (More Men, More Work)

2. Indirect Proportion: Two quantities are said to be indirectly proportional,if on the increase of the one, the other decreases to the same extent and vice-versa.

Ex. 1. The time taken by a car in covering a certain distance is inversely proportional to the speed of the car. (More speed, Less is the time taken to cover a distance)

Ex. 2. Time taken to finish a work is inversely proportional to the num of persons working at it. (More persons, Less is the time taken to finish a job)

Q:

If 20 men can build a wall 56 meters long in 6 days , what length of  a similar wall can be  built by 35 men in 3 days?

 A) 46 B) 47 C) 48 D) 49

Explanation:

Let the required length be x meters

More men, More length built     (Direct proportion)

Less days, Less length built      (Direct Proportion)

=> (20 x 6 x X)=(35 x 3 x 56)

=> x = 49

Hence, the required length is 49 m.

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Q:

A certain number of men can finish a piece of work in 100 days. If there were 10 men less, it would take 10 days more for the work to be finished. How many men were there originally?

 A) 75 B) 82 C) 100 D) 110

Explanation:

Originally let there be x men.

Less men, More days     (Indirect Proportion)

Therefore, (x-10) : x  :: 100 :110

=> (x - 10) * 110 = x * 100    => x= 110

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Q:

If 7 spiders make 7 webs in 7 days, then 1 spider will make 1 web in how many days?

 A) 1 B) 3 C) 7 D) 14

Explanation:

Let the required number days be x.

Less spiders, More days (Indirect Proportion)

Less webs, Less days (Direct Proportion)

=> 1 * 7 * x = 7 * 1 * 7

=> x= 7

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Q:

2 men and 7 boys can do a piece of work in 14 days; 3 men and 8 boys can do the same in 11 days. Then, 8 men and 6 boys can do three times the amount of this work in

 A) 18 days B) 21 days C) 24 days D) 30 days

Explanation:

(2 x 14) men +(7 x 14) boys = (3 x 11) men + (8 x 11) boys

=>5 men= 10 boys    => 1man= 2 boys

Therefore, (2 men+ 7 boys) = (2 x 2 +7) boys = 11 boys

( 8 men + 6 boys) = (8 x 2 +6) boys = 22 boys.

Let the required  number of days be x.

More boys , Less days     (Indirect proportion)

More work , More days    (Direct proportion)

Therefore, (22 * 1 * x) = (11 * 3 * 14)

=> x = 21

Hence, the required number of days = 21

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Q:

3 pumps working 8 hours a day, can empty a tank in 2 days. How many hours a day must 4 pumps work to empty the tank in 1 day?

 A) 9 B) 10 C) 11 D) 12

Explanation:

Let the required no of working hours per day be x.

More pumps , Less working hours per day  (Indirect Proportion)

Less days, More working hours per day      (Indirect Proportion)

=> (4 * 1 * x) = (3 * 2 * 8)

=> x=12

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Q:

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?

 A) 10 B) 13 C) 14 D) 15

Explanation:

Let the required number of days be x.

Less persons, More days (Indirect Proportion)

More working hours per day, Less days (Indirect Proportion)

=> 30 * 6 * x = 39 * 5 * 12

=> x= 13

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Q:

36 men can complete a piece of work in 18 days. In how many days will 27 men complete the same work ?

 A) 24 days B) 28 days C) 34 days D) 35 days

Explanation:

Less Men, means more Days {Indirect Proportion}

Let the number of days be x then,

27 : 36 :: 18 : x

[Please pay attention, we have written 27 : 36 rather than 36 : 27, in indirect proportion, if you get it then chain rule is clear to you :)]

=>27x = 36 * 18

=> x = 24

So 24 days will be required to get work done by 27 men.

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Q:

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

 A) 6 days B) 12 days C) 4 days D) 3 days

Explanation:

Let x men can do the in 12 days and the required number of days be z

More men, Less days     [Indirect Proportion]

Less work, Less days     [Direct Proportion  ]

$∴2x×1×z=x×12×12$

$⇒z=3$