# 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]$latex (m+n)\ days$

[B]$latex \left ( \frac{1}{m}\times \frac{1}{n} \right )\ days&s=1$

[C]$latex \left ( \frac{m+n}{mn} \right )\ days&s=1$

[D]$latex \left ( \frac{mn}{m+n} \right )\ days&s=1$

**$latex \mathbf{\left ( \frac{mn}{m+n} \right )\ days}&s=1$**

A’s 1 day’s work $latex = \frac{1}{m}&s=1$

B’s 1 day’s work $latex = \frac{1}{n}&s=1$

∴ (A + B)’s 1 day’s work $latex = \frac{1}{m} + \frac{1}{n} = \frac{n+m}{mn} = \frac{m+n}{mn}&s=1$

∴ Required Time $latex = \frac{mn}{m+n}&s=1$

Hence option [D] is correct answer.