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Question 27

$$M$$ man do a work in $$m$$ days. If there had been $$N$$ men more, the work would have been finished $$n$$ days earlier, then the value of $$\frac{m}{n} - \frac{M}{N}$$ is


Correct Answer: 1

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The total work is $$Mm$$ man-days, and with $$M+N$$ men it takes $$m-n$$ days, so $$Mm=(M+N)(m-n)$$. Expanding and simplifying gives $$Mn=N(m-n)$$, so $$\frac{M}{N}=\frac{m-n}{n}=\frac{m}{n}-1$$, which rearranges to $$\frac{m}{n}-\frac{M}{N}=1$$.

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