P and Q together can complete a work in 24 days. They started the work together but after 8 days P left the work. Remaining work is completed by Q in 20 more days. P alone can complete this entire work in how many days?
Show answer & explanation
Correct answer: C
Explanation
Given:
P and Q together work = 24 days
P worked = 8 days
Q completed the remaining work = 20 days
Formula:
Work = Rate × Time
P + Q's daily rate = 1/24
Work done in 8 days = 8 × (1/24) = 1/3
Remaining work = 1 − 1/3 = 2/3
Q completed 2/3 of the work in 20 days
Q's daily rate = (2/3) ÷ 20 = 1/30
P's daily rate = 1/24 − 1/30 = 1/120
P will complete the entire work alone = 120 days