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# Chain Rule

1.

A garrison of 500 men had provision for 27 days. After 3 days a reinforcement of 300 men arrived. For how many more days will the remaining food last now?

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2.

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

(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)

Boys22:11Work1 : 3⋮⋮ 14:x

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

=> x = 21

Hence, the required number of days = 21

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3.

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?

Let the required length be x meters

More men, More length built     (Direct proportion)

Less days, Less length built      (Direct Proportion)

Men20:35Days6 : 3⋮⋮ 56 :x

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

=> x = 49

Hence, the required length is 49 m.

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4.

A certain number of men can complete a piece of work in 180 days. If there are 30 men less, it will take 20 days more for the work to be completed. How many men were there originally?

Let there be x men originally.
They were to complete the work in 180 days but as the number of persons is reduced to x – 30.
∴ Work takes 20 more days. So the equation is 180x = (x – 30)200 ⇒ 20x = 6000 ⇒ x = 300.

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5.

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 :

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6.

A man completes $$\frac{5}{8}$$ of a job in 10 days. At this rate, how many more days will it take him to finish the job ?

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7.

4 mat-weavers can weave 4 mats in 4 days. At the same rate, how many mats would be woven by 8 mat-weaves in 8 days?

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8.

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?

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9.

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?

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)

Pumps4 : 3Days1 : 2⋮⋮ 8:x

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

=> x=12

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10.

A contractor undertakes to do a piece of work in 40 days. He engages 100 men at the begining 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?

[(100 x 35) + (200 x 5)]men can finish the work in 1 day

Therefore, 4500 men can finish the work in 1 day. 100 men can finish it in  4500/100= 45 days.

This is 5 days behind Schedule

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