P, Q and R working alone can complete a work in 24, 30 and 40 days respectively. All three of them started the work together but after 8 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 = 24 days
Q completes the work in = 30 days
R completes the work in = 40 days
P's work in 1 day = 1/24
Q's work in 1 day = 1/30
R's work in 1 day = 1/40
For the first 8 days, all three work together.
Combined work in 1 day = 1/24 + 1/30 + 1/40
= 5/120 + 4/120 + 3/120
= 12/120
= 1/10
Work done in 8 days = 8 × 1/10 = 4/5
Remaining work = 1 − 4/5 = 1/5
Now, P has left.
Q and R work together.
Work done in 1 day = 1/30 + 1/40
= 4/120 + 3/120
= 7/120
Let the total time taken be = x days
Q left the work 6 days before its completion.
Q worked for (x − 8 − 6) = (x − 14) days.
R worked for (x − 8) days.
4/5 + (x − 14)/30 + (x − 8)/40 = 1
96 + 4(x − 14) + 3(x − 8) = 120
96 + 4x − 56 + 3x − 24 = 120
7x + 16 = 120
7x = 104
x = 104/7 days