Question : Raja and Rocky together can complete painting work in 5 days. Together they both start painting, but after 2 days, Rocky falls sick and leaves the work. If Raja completes the remaining painting in 4 days, find the number of days in which Rocky alone can do the work.
Option 1: 12 days
Option 2: 15 days
Option 3: 20 days
Option 4: 10 days
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Correct Answer: 20 days
Solution :
Let total work = LCM of 5, 2 and 4 = 20 units
1 day's work of Raja and Rocky together = $\frac{20}{5} = 4$ units
Two days work of Raja and Rocky together = 4 × 2 = 8 units
$\therefore$ Remaining work = 20 – 8 = 12 units
1 day's work of Raja = $\frac{12}{4}$ = 3 units
1 day's work of Rocky = 4 – 3 = 1 units
$\therefore$ Time taken by Rocky to complete the work = $\frac{20}{1}$ = 20 days
Hence, the correct answer is 20 days.
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