Question

4 women and 6 men complete a task in 24 days. If the men are at least half as efficient as the women, but not more efficient than the women, what is the range of the number of days for 6 men and 2 women to complete the same task?

Answer 1

Given:

4 women and 6 men complete a task in 24 days

The men are at least half as efficient as the women, but not more efficient than the women

To find:

The range of the number of days for 6 men and 2 women to complete the same task

Solution:

Let "m" denote the men and "w" denote the women

So,

In 1 day, the amount of work done by 4w + 6m = $\frac{1}{24}$

Case (i): Considering men as at least half as efficient as the women i.e., m = ½ × w ⇒ w = 2 m:

∴ 4w + 6m = (4 × 2m) + 6m = 8m + 6m = 14 m

So, if 14m does = $\frac{1}{24}$ amount of work in 1 day

Then, amount of work done by 1m in 1 day = $\frac{1}{336}$

Now,

6m + 2w = 6m + (2×2m) = 6m + 4m = 10m

∴ In 1 day, the amount of work done by 10m will be = $\frac{10}{336}$

Or we can also say,

10 men will complete the work in = $\frac{336}{10}$ = 33.6 days

Case (ii): Considering men is as efficient as women i.e., m = w:

∴ 4w + 6m = 4m + 6m = 10 m

So, if 10m does = $\frac{1}{24}$ amount of work in 1 day

Then, amount of work done by 1m in 1 day = $\frac{1}{240}$

Now,

6m + 2w = 6m + 2m = 8m

∴ In 1 day, the amount of work done by 8m will be = $\frac{8}{240}$

Or we can also say,

8 men will complete the work in = $\frac{240}{8}$ = 30 days

∴ The range of the no. of days obtained from the above calculations of the two cases = 30 to 33.6 days

Thus, the range of the number of days for 6 men and 2 women to complete the same task is 30 to 33.6 days.

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