Chain Rule

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

1. The cost of articles is directly proportional to the nuber of articles

2. The work done is directly proportional to the number of men working at it.

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.

1. Time taken to cover a distance is inversely proportional to the speed of the car.

2. Time taken to finish a work is inversely proportional to the number of persons working at it.

Remarks : In solving questions on chain rule, we make repeated use of finding the fourth proportional. We compare every item with the term to be found out.

SOLVED PROBLEMS
1. If 20 men can build wall 56 meters long in 6 days, what length of a similar wall can be built by 35 en in 3 days.

Sol : Since the length is to be found out , we compare each item with the length is shown below.

More Men more length built (Direct)

Less days less length built (Direct)

Men 25: 35 }. .

Days 6: 3 }. . 56 : x

20 x 6 x X = 35 x 3 x 56 or x=49

Hence the required length = 49 meters.

2. If 15 men working 9 hours a can reap a field in 16 days, in how many days will 18 men reap the field, working 8 hours a day ?

Sol : Since the number of days is to be found out , we compare each item with the number of days.

More men , less days (Indirect)

Less working hours More days (Indirect)

Men 18 : 15} ..

Working Hours 8 : 9 } .. 16 : x

18 x 8 x X = 15 x 9 x 16 or x=15

Required Number of days = 15

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