Chain Rule

1. If it takes 32 days to assemble 8 cars, how long would it required to assemble 28 cars?

(a) 60

(b)  56

(c) 112

(d) 124

Answer: (c)


Let the number of days be x.

More cars, more days (direct proportion)

8:28 = 32: x


x=112 days

2. Working 14 hrs daily 12 men can complete a piece of work in 27 days. In how many days would 14 men complete the same piece of work working 9 hours daily?

(a) 18

(b) 00:00

(c) 24

(d) 36

Answer: (d)


Work done is directly proportional to the number of men working on it.

Time taken to finish a work is inversely proportional to the no. of persons working on it.

3. 30 men can produce 1500 units in 24 days 6 hours a day. In how many days, can 18 men produce 1800 units working 8 hours per day?

(a) 36

(b) 45

(c) 18

(d) 27

Answer: (a)


More men, less days (indirect proportion)

More days, more work (direct proportion)

More hours, less days (indirect proportion)

4. A contract is to be complete in 64 days, and 114 men were set to work, each working 6 hours/day. After 40 days of the work completed. How many more men may be employed to complete the work on time? Each man now working 10 hours/day?

(a) 38

(b) 159

(c) 69

(d) 140

Answer: (a)


Remaining work =

Period = 64-40=24 days

Let the total men working at be x

If men increase, working days will be decreases. (Inverse)

If men increase, working hours will be decreases (inverse)

If men increase, work done will be increases (Direct)

Additional men needed = 152 -114=38

5. A fort has provision for 300 men for 30 days. After 5 days 50 men left the fort. How long will the fort last at the same rate?

(a) 60

(b) 54

(c) 72

(d) 11

Answer: (a)


The remaining food would last 300 men (30-5) =25 days, but 50 man have left.

The remaining food would last for longer period.

6. A garrison of 4000 men had provision for 30 days. When given at the rate of 1200 gram per head. At the end of 12 days, reinforcement arrives and it was found that the provisions will last 10 days more when given at the ratio of 900 gram/head. What is the strength of the reinforcement?

(a) 2400

(b) 1600

(c) 5000

(d) 5500

Answer: (b)


Let the strength of reinforcement be x

Men increase day’s decreases. (Indirect proportion)

Less provision per head, more men (Indirect proportion)

Strength of reinforcement= (4000-2400) =1600

7. 24 men and 36 boys, working hours a day, can do a piece of work in 30 days. If a man works equal to 24 boys, then how many toys will be required to help 42 men to do twice the work in 25 days, working 9 hours a day?

(a) 42

(b) 168

(c) 84

(d) 21

Answer: (c)


1 man=2 boys

(24 men+36 boys)= (24×2+36) =84 boys

Let required no. of boy=x

42men+x boys= (42×2+x) boys= (84+x) boys

Less days, more boys (indirect proportion)

More hours per day, less boys (indirect proportion)

8. Twenty men take 21 days of 8 hours each to do a work. How many days of 6 hours each would 45 women take if 3 women do as much work as a man?





Answer: (c)


Let us take required number of days as x

Man is inversely proportional to days.

If working time decreased, day to work will be increase. (Indirect)

9. Two cogged wheels of which one has 32 cogs and the other 64, work into each other. If the latter turns 90 times in three quarters of a minute, how often does the other turn in 8 seconds?

(a) 4

(b) 8

(c) 16

(d) 32

Answer: (b)


Less cogs, more turns (indirect proportion)

Less time, less turns (indirect proportion)

10. In a diary farm, 20 cows eat 20 bags of husk in 20 days. In how many days one cow will eat one bag of husk?

(a) 1


(c) 40


Answer: (b)


More cows, less days (indirect proportion)

More bags, more days (direct proportion)

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