P, Q, and R can finish a work in 5 days, 10 days, and 15 days, respectively, working alone. P and Q work on the first day, P and R work on the second day, P and Q work on the third day, and son on till the work is completed. In how many days the work will be completed?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. .
Given that
P, Q, and R can finish a work in 5 days, 10 days, and 15 days, respectively, working alone.
Total work = LCM of (5, 10, 15) = 30
The efficiencies of
P = 30/5 = 6
Q = 30/10 = 3
R = 30/15 = 2
Now, P and Q work on the first day, P and R work on the second day, and P and Q work on the third day.
According to the question
In 3 days total work done is (6 + 3) + (6 + 2) + (6 + 3) = 26 completed
then left (30 - 26) = 4 work in next = 4/8 =1/2 days
Hence, Total work complete in (3 + 1/2) days = 7/2 days