Question : Amit can complete a piece of work in 5 hours, Jeevan and Paul together can complete it in 4 hours, while Amit and Paul together can complete it in 3 hours. Approximately, how many hours will Jeevan alone take to complete the work (rounded off to the nearest integer)?
Option 1: 5 hours
Option 2: 6 hours
Option 3: 9 hours
Option 4: 8 hours
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Correct Answer: 9 hours
Solution :
Amit can complete a task in 5 hours.
Work done by Amit in 1 day = $\frac{1}{5}$
Amit and Paul can together complete it in 3 hours.
Work done by Amit and Paul in 1 day = $\frac{1}{3}$
So, work done by Paul in 1 day = $\frac{1}{3}$ – $\frac{1}{5}$ = $\frac{2}{15}$
Jeevan and Paul together can complete it in 4 hours.
Work done by Jeevan and Paul in 1 day = $\frac{1}{4}$
$\therefore$ Work done by Jeevan in 1 day = $\frac{1}{4}$ – $\frac{2}{15}$ = $\frac{7}{60}$
So, Jeevan alone will take $\frac{60}{7}$ = 8.571 days $\approx $ 9 days
Hence, the correct answer is 9 days.
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