When quantities of different kinds are connected to one another so that we know how much of one quantity is equivalent to a given quantity of a second, etc. We can determine how much of the last kind is equivalent to a given of first kind by the chain rule.

## Proportion and Indirect Proportion

If increase or decrease of a quantity causes increase or decrease of another quantity in the same extent then, is directly proportional to

* 1)* Number of persons Amount of work done, i.e. more persons, more work

* 2)* Number of days Amount of work, i.e. more days, more work

* 3) *Working rate Amount of work, i.e. more working rate, more work

* 4) *Efficiency of man Amount of work, i.e. more efficiency of man, more work

Combining I,II,III,and IV, Amount of work. If increase of a quantity

**5)** Number of men , i.e. more the men, less the no. of days required

## Chain Rule Important Formulas

1)

Remember, “Man days” required per unit work is always same. In fact, specify the volume of job or work.

2) If in place of men there are engines burning coal for certain number of hours, then, the above equation changes to

Because, here the job of engine is to burn the coal.

3) If number of examiners examining a number of answer books in number of days by working a number of hours or day, since the job of examiner is to check the answer books,

then,

## Chain Rule Solved Examples and Solutions

**Question 1)** A garrison of 3000 men has provisions for 25 days, when given at the rate of 900 g per head. At the end of 11 days, a reinforcement arrives and it was found that now the provision will last 10 days more, when given at the rate of 840 g per head. What is the strength of reinforcement ? (MBA, ’82)

* Solution :* Let strength of reinforcement be x

Remaining food provisions after 11 days =

Total men after 11 days=(3000+x)

x=1,500.

The reinforcement had 1,500 men.

* Question 2)* Six diesel engines consume 900 litres of diesel, when each one is running for 5 h a day. How much diesel will be required by 9 engines, each running 8 h a day when 5 diesel engines of former type consume as much diesel as 8 diesel engines of the latter type.

* Solution :* Using the formula,

Since 5 diesel engines of I type=8 diesel engines of II type

= ?

(Since Amount of work = Diesel consumption)

=1,350 litres.

The diesel required is 1,350 litres

* Question 3)* Two coal loading machines each working 12 hours per day for 8 days handles 9,000 tonnes of coal with an efficiency of 90%. While 3 other coal loading machines at an efficiency of 80% set to handle 12,000 tonnes of coal in 6 days. Find how many hours per day each should work.

* Solution:* Here

=

Each machine should work

* Question 4)* ’A’ can do a piece of work in days which ‘B’ can do in days. If ‘A’ wages are Rs.50 per week and ‘B’ wages are Rs.42.50 per week, what ‘A’ would have charged for doing a piece of work for which B received Rs 340? (ITI, ’90)

*Total wage = Total Amount of work; Wage rate = work Rate*

**Solution :**

= 300

‘A’ should charge Rs 300 for the job.

* Question 5)* Four lorries carrying 4 tons each move 128 tons in 8 days. In how many days will 6 tons in 8 days. In how many days will 6 lorries carrying 3 tons each move 540 tons ?

**Solution :**

= 30 days.

## Chain Rule Questions from previous year exams

chain rule aptitude

## Chain Rule Important Videos - Must Watch

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