A piece of work can be done by 6 men and 5 women in 6 days or 3 men and 4 women in 10 days. It can be done by 9 men and 15 women in how many days ?

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Solution

To calculate the answer we need to get 1 man per day work and 1 woman per day work.
Let 1 man 1 day work $= x$ and 1 woman 1 days work $= y .$ => $6 x + 5 y$ = $\frac{1}{6}$ and $3 x + 4 y$ = $\frac{1}{10}$
On solving we get x = $\frac{1}{54}$ and y = $\frac{1}{90}$
(9 men + 15 women)'s 1 days work = $\frac{9}{54}$ + $\frac{15}{90}$ = $\frac{1}{3}$

9 men and 15 women will finish the work in $3$ days

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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.

8 women or 6 men can finish a piece of construction work in 12 days. 4 women and 9 men will finish the same work in ___days.

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