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)**

**Explanation:**

Let the number of days be x**.**

More cars, more days (direct proportion)

8:28 = 32: x

8x=28×32

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)**

**Explanation:**

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)**

**Explanation:**

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)**

**Explanation:**

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)**

**Explanation:**

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)**

**Explanation:**

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)**

**Explanation:**

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?

**(a) **

**(b) **

**(c) **

**(d)**

**Answer: (c)**

**Explanation:**

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)**

**Explanation:**

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

**(b) **

**(c) **40

**(d)**20

**Answer: (b)**

**Explanation:**

More cows, less days (indirect proportion)

More bags, more days (direct proportion)