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Question

If 12 men and 16 boys can do a piece of work in 5 days, 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is :


A
2:1
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B
3:1
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C
3:2
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D
5:4
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Solution

The correct option is D $$2 : 1$$
Let $$1$$ man's $$1$$ day's work be $$x$$ and $$1$$ boy's $$1$$ day's work be $$y$$.

Then,
$$12x+16y=\dfrac{1}{5}$$     .....(1)

$$13x+24y=\dfrac{1}{4}$$     .....(2)

Solving equation (1) and (2), we get,

$$x=\dfrac{1}{100}$$ and $$y=\dfrac{1}{200}$$

Required ratio $$ = \dfrac{1}{100} : \dfrac{1}{200} = 2: 1$$

Mathematics

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