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6 men can complete a work in 64 days. 24 women can complete the same work in 32 days. 16 men and 24 women together worked for 12 days, after which 8 men and 8 women were dropped. In how many days the work will be completed?

6 men can complete a work in 64 days. 24 women can complete the same work in 32 days. 16 men and 24 women together worked for 12 days, after which 8 men and 8 women were dropped. In how many days the work will be completed? Correct Answer 15

Given:

Total time taken by 6 men to complete the work = 64 days

Total time taken by 24 women to complete the work = 32 days

Formula used:

Total work = Total efficiency × Total time

Calculation:

Let, M = Man and W = Woman

So, 6M × 64 = 24W × 32

⇒ M/W = 2/1

∴ A man can do in a day = 2 work

∴ A woman can do in a day = 1 work

Total work = (24 × 1) × 32 = 768

The total work by 16 men and 24 women for 12 days =  × 12

= 12 (32 + 24)

The total work done by 8 men and 16 women for one day = (8 × 2) + (16 × 1) = 32

Suppose, the total time is taken by  8 men and 16 women = x

Then, 12 (32 + 24) + 32x = 768

⇒ (12 × 56) + 32x = 768

⇒ 32x = 768 - 672

⇒ 32x = 96

⇒ x = 96/32 = 3

∴ Total required time = 12 + 3 = 15 days

∴ The work will be completed in 15 days.

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