LIC AAO 06 Mar 2016 Paper

Part of work done by 14 men in 3 days = ${\mathit{W}}_2$
${\mathit{W}}_1$ = 1
∴ $\frac{{\mathit{M}}_1{\mathit{D}}_1}{{\mathit{W}}_1}$ = $\frac{{\mathit{M}}_2{\mathit{D}}_2}{{\mathit{W}}_2}$
⇒ $\frac{8\times 21}{1}$ = $\frac{14\times 3}{{\mathit{W}}_2}$
⇒ 8 × 21 × ${\mathit{W}}_2$ = 14 × 3
⇒ ${\mathit{W}}_2$ = $\frac{14\times 3}{8\times 21}$ = $\frac{1}{4}$
∴ Remaining work = 1 - $\frac{1}{4}$ = $\frac{3}{4}$
Time taken by 9 women in doing $\frac{3}{4}$ th work = 24 days
∴ Time taken by them in doing whole work = $\frac{24\times 4}{3}$ = 32 days