Exams › SSC CGL (Prelims) › General

P and Q together can complete a job in 16 days. Q and R together can complete it in 24 days, and R and P together can do it in 32 days. In how many days can P alone complete the job?

1. 30 1/2 days
2. 32 days
3. 38 2/5 days
4. 48 days

Correct answer: 38 2/5 days

Solution

Let daily work rates be P, Q, and R. Then \(P+Q=1/16\), \(Q+R=1/24\), and \(R+P=1/32\). Adding gives \(2(P+Q+R)=1/16+1/24+1/32=13/96\), so \(P+Q+R=13/192\). Hence \(P=(P+Q+R)-(Q+R)=13/192-1/24=5/192\), so P alone takes \(192/5=38\frac{2}{5}\) days.

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