8 men can complete a work in 45 days. 8 women can complete the same work in 18 days. In how many days will 5 men and 8 women, together, complete the same work?

The correct answer is 14 $\frac{2}{5}$ days.

We are given:

- 8 men can complete the work in 45 days.
- 8 women can complete the same work in 18 days.
- We need to find how many days 5 men and 8 women together will take.

Step 1: Find the work done by 1 man per day (1 man's daily work rate)

If 8 men complete the work in 45 days, then total work = 8 × 45 = 360 man-days.

So, 1 man's 1 day work =

$\frac{1}{360}$

Step 2: Find the work done by 1 woman per day (1 woman's daily work rate)

If 8 women complete the work in 18 days, then total work = 8 × 18 = 144 woman-days.

So, 1 woman's 1 day work =

$\frac{1}{144}$

Step 3: Find the combined 1 day work of 5 men and 8 women

Work done by 5 men in 1 day:

$\frac{5}{360}$ = $\frac{1}{72}$

Work done by 8 women in 1 day:

$\frac{8}{144}$ = $\frac{1}{18}$

Combined 1 day work of 5 men + 8 women:

$\frac{1}{72}$ + $\frac{1}{18}$

Finding the LCM of 72 and 18, which is 72:

$\frac{1}{72}$ + $\frac{4}{72}$ = $\frac{5}{72}$

Step 4: Find the total number of days required

If they together complete $\frac{5}{72}$ of the work in 1 day, then they will complete the full work in:

$\frac{72}{5}$ = 14.4 days = 14 $\frac{2}{5}$ days

Therefore, 5 men and 8 women together will complete the work in 14 $\frac{2}{5}$ days.