SSC CHSL 15 Nov 2015 Shift 2 Paper

Let total work to be done = $5\mathit{y}$ units
Let B's efficiency = $\mathit{x}$ units/day
⇒ A's efficiency = $3\mathit{x}$ units/day
Work done by (A+B) together in 1 day = $\left(\mathit{x}+3\mathit{x}\right)=4\mathit{x}$ units/day
⇒ Work done in 9 days $=9\times 4\mathit{x}=36\mathit{x}$ units --------(i)
Also, according to ques, work done in 9 days = $\frac{2}{5}\times 5\mathit{y}=2\mathit{y}$ units -----(ii)
⇒ $36\mathit{x}=2\mathit{y}$
⇒ $\frac{\mathit{y}}{\mathit{x}}=\frac{36}{2}=18$ --(iii)
∴ Number of days by which B can do the work alone = $\frac{5\mathit{y}}{\mathit{x}}$
= $5\times \frac{\mathit{y}}{\mathit{x}}=5\times 18=90$ days