SSC CGL 16 Aug 2015 Shift 2 Paper

Let time taken by A = x days
∴ Time taken by B = 2x days
Time taken by C = 3x days
According to the question,
$\frac{1}{\mathit{x}}+\frac{1}{2\mathit{x}}+\frac{1}{3\mathit{x}}$ = $\frac{1}{6}$
⇒ $\frac{6+3+2}{6\mathit{x}}$ = $\frac{1}{6}$
⇒ $\frac{11}{6\mathit{x}}$ = $\frac{1}{6}$ ⇒ 6x = 6 × 11
⇒ x = $\frac{6\times 11}{6}$ = 11
∴ Time taken by C alone = 3x
= 3 × 11 = 33 days