LIC AAO 04 May 2019 Paper

(2) Ratio of the efficiencies of A and B = 3 : 4
∴ Ratio of time taken = 4 : 3
∴ (A + B)’s 1 day’s work = $\frac{1}{8}$
∴ $\frac{1}{4\mathit{x}}+\frac{1}{3\mathit{x}}=\frac{1}{8}$
⇒ $\frac{3+4}{12\mathit{x}}=\frac{1}{8}$
⇒ $12\mathit{x}=8\times 7$
⇒ $\mathit{x}=\frac{8\times 7}{12}=\frac{14}{3}$
∴ Time taken byA = $\frac{56}{3}$ days
Time taken by B $=\frac{14}{3}\times 3=14$ days
(A + B)’s 2 days’ work = $2\left(\frac{3}{56}+\frac{1}{14}\right)$
= $2\left(\frac{3+4}{56}\right)=2\times \frac{7}{56}=\frac{1}{4}$
Remaining work $=1-\frac{1}{4}=\frac{3}{4}$
Let time taken by C alone in doing whole work be y days.
(B + C)’s 6 days’work =$\frac{3}{4}$
⇒ $\frac{6}{14}+\frac{6}{\mathit{y}}=\frac{3}{4}\Rightarrow \frac{6}{\mathit{y}}=\frac{3}{4}-\frac{3}{7}$
⇒ $\frac{6}{\mathit{y}}=\frac{21-12}{28}\Rightarrow \frac{6}{\mathit{y}}=\frac{9}{28}$
⇒ $\mathit{y}=\frac{28\times 6}{9}=\frac{56}{3}$ days