Question : Ganesh, Ram, and Sohan can complete a work in 16 days. If Ganesh and Ram together can complete the same work in 24 days, the number of days Sohan alone takes to finish the work is:
Option 1: 40
Option 2: 48
Option 3: 32
Option 4: 30
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Correct Answer: 48
Solution : Given: Time taken by Ganesh, Ram, and Sohan together to complete the work = 16 days ⇒ Part of work done by Ganesh, Ram, and Sohan in a day = $\frac{1}{16}$ Time taken by Ganesh and Ram to complete the work = 24 days ⇒ Part of work done by Ganesh and Ram in a day = $\frac{1}{24}$ Let the time taken by Sohan alone to do the job = $x$ days ⇒ Part of the job done by Sohan alone in 1 day = $\frac{1}{x}$ So, $\frac{1}{24}$ + $\frac{1}{x}$ = $\frac{1}{16}$ ⇒ $\frac{1}{x}$ = $\frac{1}{16}$ – $\frac{1}{24}$ = $\frac{3 - 2}{48}$ = $\frac{1}{48}$ Therefore, the time taken by Sohan alone to complete the work = $x$ = 48 days Hence, the correct answer is 48.
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