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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