A can complete a work in ‘m’ days and B can complete it in ‘n’ days. How many days will it take to complete the work if both A and B work together ?

A can complete a work in ‘m’ days and B can complete it in ‘n’ days. How many days will it take to complete the work if both A and B work together ?
[A](m+n)\ days
[B]\left ( \frac{1}{m}\times \frac{1}{n} \right )\ days
[C]\left ( \frac{m+n}{mn} \right )\ days
[D]\left ( \frac{mn}{m+n} \right )\ days

\mathbf{\left ( \frac{mn}{m+n} \right )\ days}
A’s 1 day’s work = \frac{1}{m}
B’s 1 day’s work = \frac{1}{n}
∴ (A + B)’s 1 day’s work = \frac{1}{m} + \frac{1}{n} = \frac{n+m}{mn} = \frac{m+n}{mn}
∴ Required Time = \frac{mn}{m+n}
Hence option [D] is correct answer.

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