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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


Team Careers360 1st Jan, 2024
Answer (1)
Team Careers360 2nd Jan, 2024

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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