Question

Solve this:
Q.26. Six men and 4 women can do a piece of work in 32 days. Seven men and 12 women can do it in 18 days. In how many days can 18 men and 8 women do the same work, working together?
(a) 10
(b) 12
(c) 14
(d) 16

Answer 1

Dear student
$$\begin{gathered} \mathrm{Let}1\mathrm{man}\text{'}\mathrm{s}1\mathrm{day}\text{'}\mathrm{s}\mathrm{work}=\mathrm{x} \\ \mathrm{and}1\mathrm{women}\text{'}\mathrm{s}1\mathrm{day}\text{'}\mathrm{s}\mathrm{work}=\mathrm{y} \\ \mathrm{then}6\mathrm{x}+4\mathrm{y}=\frac{1}{32}...\left(1\right) \\ \mathrm{and}7\mathrm{x}+12\mathrm{y}=\frac{1}{18}...\left(2\right) \\ \mathrm{multiplying}\left(1\right)\mathrm{by}7\mathrm{and}\left(2\right)\mathrm{by}6,\mathrm{we}\mathrm{get} \\ 42\mathrm{x}+28\mathrm{y}=\frac{7}{32}....\left(3\right) \\ 42\mathrm{x}+72\mathrm{y}=\frac{1}{3}...\left(4\right) \\ \mathrm{Subtracting}\left(3\right)\mathrm{from}\left(4\right),\mathrm{we}\mathrm{get} \\ 42\mathrm{x}+72\mathrm{y}-42\mathrm{x}-28\mathrm{y}=\frac{1}{3}-\frac{7}{32} \\ \Rightarrow 44\mathrm{y}=\frac{11}{96} \\ \Rightarrow \mathrm{y}=\frac{1}{384} \\ \mathrm{Put}\mathrm{the}\mathrm{value}\mathrm{of}\mathrm{y}\mathrm{in}\left(3\right),\mathrm{we}\mathrm{get} \\ 42\mathrm{x}+28\left(\frac{1}{384}\right)=\frac{7}{32} \\ \Rightarrow 42\mathrm{x}+\frac{7}{96}=\frac{7}{32} \\ \Rightarrow 42\mathrm{x}=\frac{7}{48} \\ \Rightarrow \mathrm{x}=\frac{1}{288} \\ \mathrm{So},(18\mathrm{men}\mathrm{and}8\mathrm{women})1\mathrm{day}\text{'}\mathrm{s}\mathrm{work}=\frac{18}{288}+\frac{8}{384}=\frac{1}{12} \\ \mathrm{Therefore},18\mathrm{men}\mathrm{and}8\mathrm{women}\mathrm{can}\mathrm{do}\mathrm{the}\mathrm{work}\mathrm{in}12\mathrm{days}. \end{gathered}$$
Regards