The work of 4 men is equal to work of 6 women and the work of 9 women is equal to work of 12 boys. 8 men and 6 women working 8 hours a day complete a work is 15 days. In how many days 2 men, 3 women and 4 boys together working 6 hours daily will complete that work?

The work of 4 men is equal to work of 6 women and the work of 9 women is equal to work of 12 boys. 8 men and 6 women working 8 hours a day complete a work is 15 days. In how many days 2 men, 3 women and 4 boys together working 6 hours daily will complete that work? Correct Answer 40

Given:

The work of 4 men is equal to work of 6 women and the work of 9 women is equal to work of 12 boys.

8 men and 6 women working 8 hours a day complete a work is 15 days.

Assumption:

Efficiency of a man = M unit work/hour.

Efficiency of a woman = W unit work/hour & efficiency of a boy = B unit work/hour.

Calculation:

⇒ 4M = 6W

⇒ 2M = 3W

The work of 9 women is equal to work of 12 boys.

⇒ 9W = 12B

⇒ 3W = 4B

∴ 2M = 3W = 4B

In 1 day, working 8 hours per day, total work done by 1 man = 8M

In 1 day, working 8 hours per day, total work done by 1 woman = 6W

8 men and 6 women working 8 hours a day complete a work is 15 days.

∴ Total work = (8M × 8 × 15) + (6W × 8 × 15) = 240 × (4M + 3W)

Assume that, in n days, 2 men, 3 women and 4 boys together working 6 hours daily will completer that work.

Total work done in this case = (2 × M × 6 × n) + (3 × W × 6 × n) + (4 × B × 6 × n)

In both cases total work will be equal.

⇒ (12M + 18W + 24B) × n = 240 × (4M + 3W)

⇒ 6 × (2M + 3W + 4B) × n = 240 × (4M + 3W)

⇒ (2M + 3W + 4B) × n = 40 × (4M + 3W)

⇒ (3W + 3W + 3W) × n = 40 × (6W + 3W)

⇒ n = 40