Exams › SSC CGL (Prelims) › General

P, Q, and R can complete a certain work in 24, 36, and 72 days, respectively. How many days will it take for P to finish the work if he receives help from Q and R every fourth day?

1. 16 days
2. 17 days
3. 18 days
4. 19 days

Correct answer: 19 days

Solution

P’s 1-day work = \(1/24\), Q’s = \(1/36\), and R’s = \(1/72\). In every 4-day cycle, P works 4 days and gets help from Q and R on the 4th day, so total work per cycle is \(3\cdot\frac{1}{24}+\left(\frac{1}{24}+\frac{1}{36}+\frac{1}{72}\right)=\frac{1}{8}+\frac{1}{12}=\frac{5}{24}\). After 4 such cycles, 20 days, the work would exceed 1, so the exact completion occurs on day 19.

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