P and Q alone can complete a work in 12 days and 18 days respectively. 50% of the work is completed by R alone in 2n days and the remaining work is completed by P and Q working together in n days. Find the time taken by Q and R to complete the whole work, while working together.
A. 4 days
B. 8 days
C. 12 days
D. 14 days
E. None of these
Sol:
Time taken by P and Q to complete the work =
(12 * 18)/(12 + 18) = 7.2 days
n = 7.2/2 = 3.6 (Since P and Q complete 50% of
work)
Time taken by R aloneto complete 50% of work =
2n = 7.2 days
Time taken by R aloneto complete whole work =
7.2 * 2 = 14.4 days
Time taken by Q and R to complete the work
together = (18 * 14.4)/(18 + 14.4)
= 8 days
