P alone can complete 50% of a piece of work in 6 days, and Q can complete 50% of the same work in 9 days. With the help of R, they finish the work in 6 days. In how many days can R alone complete 25% of the work?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 9.
P can complete the whole work in 12 days
Q can complete the whole work in 18 days
P + Q + R can complete the whole work in 6 days
LCM(12, 18, and 6) = 36
The efficiency of P = 36/12 = 3 units
The efficiency of Q = 36/18 = 2 units
The efficiency of (P + Q + R) = 36/6 = 6 days
The efficiency of R = 6 - 3 - 2 = 1 unit
⇒ 25% of 36 = 9 units
Time taken by R = 9/1 = 9 days