A alone can do a work in 15 days. B alone can do the same work in 20 days. C alone can do the same work in 30 days. They started the work together. B left after 2 days. A and C together completed the remaining work. In how many days remaining work was completed?
Show answer & explanation
Correct answer: C
Explanation
Given:
A = 15 days, B = 20 days, C = 30 days
B left the work after 2 days.
A's rate = 1/15, B = 1/20, C = 1/30
Work done in the first 2 days:
(1/15 + 1/20 + 1/30) × 2
= (4+3+2)/60 × 2
= 9/60 × 2 = 18/60 = 3/10
Remaining work = 1 − 3/10 = 7/10
Now, the combined rate of A + C = 1/15 + 1/30
= (2+1)/30 = 3/30 = 1/10
Time = (7/10) / (1/10) = 7 days