Question : Ramesh alone can complete a work in 24 days. Ramesh and Somesh can complete it in 8 days. How long will Somesh alone take to complete the work?
Option 1: 10 days
Option 2: 15 days
Option 3: 14 days
Option 4: 12 days
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Correct Answer: 12 days
Solution : Time taken by Ramesh and Somesh to complete the work = 8 days ⇒ Part of work done by Ramesh and Somesh together in a day = $\frac{1}{8}$ Time taken by Ramesh alone to complete the work = 24 days ⇒ Part of work done by Ramesh alone in a day = $\frac{1}{24}$ Let the time taken by Somesh alone to complete the work = $x$ days ⇒ Part of work done by Somesh alone in a day = $\frac{1}{x}$ ⇒ $\frac{1}{24} + \frac{1}{x} = \frac{1}{8}$ ⇒ $\frac{1}{x} = \frac{1}{8}–\frac{1}{24} = \frac{3–1}{24} = \frac{1}{12}$ ⇒ Time taken by Somesh alone to complete the work = 12 days Hence, the correct answer is 12 days.
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