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Question 138
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 ?
Solution
Let the total work be $$mn$$ units
=> Rate at which A completes the work = $$\frac{mn}{m} = n$$ units/day
=> Rate at which B completes the work = $$\frac{mn}{n} = m$$ units/day
=> Rate at which both A & B work together = $$(m+n)$$ units/day
=> No. of days required by both of them to complete the work = $$\frac{mn}{m+n}$$ days
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