Question : Ram and Ramesh can do work in 12 days, Ramesh and Somesh in 15 days and Somesh and Ram in 10 days. If Ram, Ramesh, and Somesh work together, in how many days will they complete the work?
Option 1: 10
Option 2: 8
Option 3: 12
Option 4: 6
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Correct Answer: 8
Solution :
One day work of Ram and Ramesh = $\frac{1}{12}$
One day work of Ramesh and Somesh = $\frac{1}{15}$
One day work of Somesh and Ram = $\frac{1}{10}$
⇒ 2[(Ram + Ramesh + Somesh)'s one day's work] = $\frac{1}{12}+\frac{1}{15}+\frac{1}{10}$
⇒ 2[(Ram + Ramesh + Somesh)'s one day's work] = $\frac{5+4+6}{60}$
⇒ (Ram + Ramesh + Somesh)'s one day's work = $\frac{15}{2×60}$ = $\frac{15}{120}$ = $\frac{1}{8}$
So, the work was completed by Ram, Ramesh, and Somesh altogether in 8 days.
Hence, the correct answer is 8.
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