Question

If 7 men or 8 women or 10 boys can finish a piece of work in 24 days of 9 h, find how many men with the help of 4 women and 5 boys can finish it in 18 days of 6 h? (1) 10 men (2) 12 men (3) 7 men (4) 6 men (5) None of these​

Answer 1

Answer:

7 men

Explanation:

Find the amount of work 4 women can do in 1 hour:

8 women = 24 days of 9 hours = 216 hours

1 woman = 216 x 8 = 1728 hours

4 women = 1728 ÷ 4 = 432 hours

⇒ So 4 women can do 1/432 amount of work in 1 hour

Find the amount of work 5 boys can do in an hour:

10 boys = 24 days of 9 hours = 216 hours

1 boy = 216 x 10 = 2160 hours

5 boys = 2160 ÷ 5 = 432 hours

⇒ So 5 boys can do 1/432 amount of work in 1 hour

Find the amount of work 4 women and 5 boys can do in 18 days of 6 hours:

18 days of 6 hours = 108 hours

4 women, 1 hour = 1/432 amount of work

4 women, 108 hour = 1/432 x 108 = 1/4  amount of work

10 boys, 1 hour = 1/432 amount of work

10 boys, 108 hour = 1/432 x 108 = 1/4  amount of work

Total work = 1/4 + 1/4 = 1/2

⇒ 4 women and 5 boys can do 1/2 the work in 18 days of 6 hours

Find the remaining of the work:

Remaining work = 1 - 1/2 = 1/2

Find the number of days the men need:

7 men = 24 days of 9 hours = 24 x 9 = 216 hours

1 man = 216 x 7 = 1512 hours

⇒ 1 man can do 1/1512 of the work in 1 hour

1 hour = 1/1512 of the work

108 hours = 1/512 x 108 = 1/14 of the work

Number of men needed = 1/2 ÷ 1/14 = 7