SSC CHSL 6 Mar 2018 Shift 3 Paper

Let the total work to be done = L.C.M.(15,24) = 120 units
P can complete the work in 15 days, ⇒ P's efficiency = $\frac{120}{15}=8$units/day
Similarly, Q's efficiency = $\frac{120}{24}=5$ units/day
Let the work is completed in days, thus P worked for t dayeswhile Q for $\left(\mathit{t}-2\right)$ days
⇒ $8\left(\mathit{t}\right)+5\left(\mathit{t}-2\right)=120$
⇒ $8\mathit{t}+5\mathit{t}-10=120$
⇒ $13\mathit{t}=120+10=130$
⇒ $\mathit{t}=\frac{130}{13}=10$
∴ The work is completed in 10 days.