IBPS Clerk Mains 2019 Paper

(a) Quantity A : Let total units of work = 120 units (LCM of 12, 15and 24) ⇒ Efficiency of P and Q together = $\frac{120}{12}=10$ ⇒Efficiency of Q and R together = $\frac{120}{15}=8$ ⇒ Efficiency of R and P together = $\frac{120}{24}=5$ ⇒ Efficiency of P, Q and R together = $\frac{10+8+5}{2}$ = $\frac{23}{2}$ days ⇒ Efficiency of Q = $\frac{23}{2} - 5 = \frac{13}{2}$ ⇒ Time taken by Q to finish the work alone $=\frac{120 \times 2}{13}$ days = $\frac{240}{13}$ days Quantity B : Let total units of work = 30 units (LCM of 10 and 15) ⇒ Efficiency of S = $\frac{30}{10}=3$ ⇒ Efficiency of T = $\frac{60}{15}=2$ Since S left after 5 days. Unit of work left after 5 days = $30 - 5 \times (3 + 2) = 5$ units ⇒ Time taken by T to finish the remaining work = $\frac{5}{2}=2.5$ days ⇒ Total time to finish the whole work = 5 + 2.5 days = 7.5 days ∴ Quantity A > Quantity B