P, Q and R working alone can complete a work in 15, 20 and 30 days respectively. All three of them started the work together but after 4 days P left the work. Q left the work 6 days before the work was completed. R completed the remaining work alone. In how many days was the total work completed?
Show answer & explanation
Correct answer: B
Explanation
Given:
P completes the work in = 15 days
Q completes the work in = 20 days
R completes the work in = 30 days
P's 1-day work = 1/15
Q's 1-day work = 1/20
R's 1-day work = 1/30
For the first 4 days, all three work together.
Combined 1-day work
= 1/15 + 1/20 + 1/30
= 4/60 + 3/60 + 2/60
= 9/60
= 3/20
Work done in 4 days = 4 × 3/20 = 3/5
Remaining work = 1 − 3/5 = 2/5
Now, P has left.
Q and R work together.
1-day work = 1/20 + 1/30
= 3/60 + 2/60
= 5/60
= 1/12
Let the total time taken be = x days
Q left the work 6 days before its completion.
Q worked for (x − 4 − 6) = (x − 10) days.
R worked for (x − 4) days.
3/5 + (x − 10)/20 + (x − 4)/30 = 1
36 + 3(x − 10) + 2(x − 4) = 60
36 + 3x − 30 + 2x − 8 = 60
5x − 2 = 60
5x = 62
x = 62/5 days