Exams › SSC CGL (Prelims) › General

P can complete a task in 6 days, and Q can destroy it in 4 days. P works for 3 days, then Q joins for 2 days. In how many days will P finish the remaining work alone?

1. 6 days
2. 7.5 days
3. 4 days
4. 9 days

Correct answer: 4 days

Solution

P’s rate is $1/6$ per day and Q’s rate is $-1/4$ per day. In 3 days P completes $1/2$ work; in the next 2 days, together they do $2(1/6-1/4)=-1/6$ work, so remaining work is $1/2+1/6=2/3$. P alone needs $(2/3)/(1/6)=4$ days.

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