**Question 6:**

12 men and 16 boys can do a piece of work in 5 days and 13 men and 24 boys can do it in 4 days. Compare the daily work done by a man with that done by a boy.

[1] 3 : 2

[2] 2 : 1

[3] 4 : 7

[4] 3 : 1

**Answer:**

**Explanation: **

12 men + 16 boys can do the work in 5 days.

5 x (12 men + 16 boys) can do the work in 1 day.

Similarly 4 x (13 men + 24 boys) can do the same work in 1 day.

=> 52 men + 96 boys = 60 men + 80 boys.

=> 8 men = 16 boys or 1 man = 2 boys, i.e. 2 : 1

**Question 7:**

If 5 men and 3 boys can reap 23 hectares in 4 days and if 3 men and 2 boys can reap 7 hectares in 2 days, then how many boys must assist 7 men in order that they may reap 45 hectares in 6 days?

[1] 1

[2] 2

[3] 3

[4] 4

**Answer:**

**Explanation: **

5 men + 3 boys can reap 23 hectares in 4 days.

3 men + 2 boys can reap 7 hectares in 2 days.

14 (5 men + 3 boys) can reap 23 x 14 hectares in 4 days.

23 (3 men + 2 boys) can reap 7 x 2 x 23 hectares in 4 days.

14 (5 men + 3 boys) = 23 (3 men + 2 boys).

1 man = 4 boys. Now 5 men + 3 boys = 23 boys.

23 boys can reap 23 hectares in 4 days.

30 boys can reap 45 hectares in 6 days.

But 30 boys = 28 boys + 2 boys = 7 men + 2 boys.

Hence 2 boys must assist 7 men.

**Question 8:**

X can do a job in 10 days, Y in 15 days and Z in 18 days. Y and Z begin the work but have to leave after 3 days. How many days will X take to finish the job?

[1] 57/9 days

[2] 57/11 days

[3] 53/12 days

[4] 6.5 days

**Answer:**

**Explanation: **

(Y + Z)'s one day's work = 1/15 + 1/18 = 11/90.

(Y + Z)'s 3 day's work = 1/15 + 1/18 = 33/90.

Remaining Work = 1 — 33/90 = 57/90. ,

Time taken by X = 57/90 ÷ 1/10 = 57/9 days.

**Question 9:**

10 men and 12 children complete a certain piece of work in 10 days. Each child takes thrice the time taken by a man to complete the work. The time taken by 12 men to finish the same work is

[1] 11.66 days

[2] 10 days

[3] 10.33 days

[4] 12.16 days

**Answer:**

**Explanation: **

3 Children = 1 Man; 10 Men + 12 Children = 10 Men + 4 Men = 14 Men.

Work = 14 x 10 = 12 x D where D is the required number of days.

D = 14 x 10/12 = 140/12 days = 11.66 days.

**Question 10:**

5 men and 8 women can do a job in 8 days, while 4 men and 6 women can do it in 10 days. How many days will 10 women take to finish the job?

[1] 10 days

[2] 40 days

[3] 20 days

[4] None of these

**Answer:**

**Explanation: **

Let X = 1 man's one day's job, Let Y = 1 woman's one day's job.

According to the given condition, 5X + 8Y = 1/8 and 4X + 6Y = 1/10.

On solving the two equations, we get : X = 1/40, Y = 0.

Women have not done any amount of work.

Women can never complete the work.