P, Q and R together can do a piece of work in 56 days. P and Q together can do one-fourth as much work as R alone. In how many days P and Q together complete the entire work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is option 3 i.e. 280.
Let total work = 1 unit
P + Q + R can do it in 56 days
(P + Q + R)'s efficiency = 1/56
(P + Q) = ¼ × R → P + Q = R/4
Substitute into (P + Q + R):
(P + Q) + R = R/4 + R = (5R)/4
5R/4 = 1/56
⇒ R = 4/(5 × 56) = 1/70
P + Q = R/4 = (1/70)/4 = 1/280
So, P + Q alone take = 280 days