P and Q can do a piece of work in 20 days and 30 days, respectively. They work together for 6 days, and then Q is replaced by R. If the rest of the work is completed by P and R in 8 more days, in how many days can R alone complete 60% of the work?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. 48 days.
P's rate = 1/20
Q's rate = 1/30
P and Q together in 1 day = 1/20 + 1/30 = 1/12
In 6 days, work done = 6/12 = 1/2
Remaining work = 1 - 1/2 = 1/2
Work done by P and R in 8 days = 1/2
1 day of work of P and R = 1/16
R’s 1-day work = 1/16 - 1/20 = 1/80
So, R completed the work in 80 days.
60% of work = 60/100 = 0.6
Time required for R alone = 0.6 ÷ (1/80) = 0.6 × 80 = 48 days