SSC CHSL 15 Nov 2015 Shift 1 Paper

Let total work to be done = L.C.M. (24,16) = 48 units
X can do a piece of work in 24 days, => X's efficiency = $\frac{48}{24}=2$ units/day
Let Y's 1 day work = $\mathit{y}$ units/day
Now, X worked for 16 days and Y worked for (16-4) = 12 days
⇒ $2\left(16\right)+\mathit{y}\left(12\right)=48$
⇒ $32+12\mathit{y}=48$
⇒ $12\mathit{y}=48-32=16$
⇒ $\mathit{y}=\frac{16}{12}=\frac{4}{3}$
∴ Y can finish the work in = $\frac{48}{\frac{4}{3}}$
= $48\times \frac{3}{4}=36$ days