Question

6 men and 9 women can do a piece of work in 4 days. 4 men and 4 women can do it in 8 days. How many days can 20 men and 6 women do the same work

Answer 1

Dear Student,

Let 1 man's 1 day's work = x and 1 women's 1 day's work = y

then 6x+9y=$\frac{1}{4}$ ---(1) and 4x+4y=$\frac{1}{8}$ ---(2)

Multiplying (1) by 2 and (2) by 3 we get

$$\begin{gathered} 12\mathrm{x}+18\mathrm{y}=\frac{2}{4}.....\left(3\right) \\ 12\mathrm{x}+12\mathrm{y}=\frac{3}{8}......\left(4\right) \\ \mathrm{Subtracting}\left(4\right)\mathrm{from}\left(3\right),\mathrm{we}\mathrm{get} \\ 6\mathrm{y}=\frac{2}{4}-\frac{3}{8} \\ \Rightarrow 6\mathrm{y}=\frac{4-3}{8} \\ \Rightarrow \mathrm{y}=\frac{1}{48} \\ \mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{y}\mathrm{in}\left(3\right),\mathrm{we}\mathrm{get} \\ 12\mathrm{x}+18\times \frac{1}{48}=\frac{2}{4} \\ \Rightarrow 12\mathrm{x}+\frac{3}{8}=\frac{1}{2} \\ \Rightarrow 12\mathrm{x}=\frac{1}{2}-\frac{3}{8} \\ \Rightarrow 12\mathrm{x}=\frac{4-3}{8} \\ \Rightarrow \mathrm{x}=\frac{1}{96} \end{gathered}$$

(20 men and 6 women) 1 day's work = $\frac{20}{96}+\frac{6}{48}=\frac{32}{96}=\frac{1}{3}$
Therefore 20 men and 6 women can do the work in 3 days.

Regards