Question

A particular work can be completed by 6 men and 6 women in 24 days; whereas the same work can be completed by 8 men and 12 women in 15 days. Find:

i) According to the amount of work done, one man is equivalent to how many women.

ii) The time taken by 4 men and 6 women to complete the same work.

Answer 1

6 men + 6 women can finish the work in = 24 days
144 men + 144 women can finish it in = 1 day
8 m + 12 women can finish the work in = 15 days
120 men + 180 women can finish it in = 1 day.
i) $\therefore$ 144 men + 144 women= 120 men + 180 women
$\Rightarrow$ 144 men - 120 men= 180 - women - 144 women
$\Rightarrow$ 24 men = 36 women
1 man $=\frac{36}{24}$
$=\frac{3}{2}$ women
$=1\frac{1}{2}$ women

ii) In first case, given 6 men+6 women can do a work in 24 days.
$6\times \frac{3}{2}+6=9+6$ [Since, 1 man=$\frac{3}{2}$ women]
= 15 women can complete a work in 24 days.
Now, we need to find:
$4\times \frac{3}{2}+6$
= 6 + 6
= 12
Now, 15 women can do a piece of work in = 24 days.
1 woman will do it in $=24\times 15$ days
and 12 women will do it in
$=\frac{24\times 15}{12}$
= 30 days.