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Question

If 1 man or 2 women or 3 boys can do a piece of work in 44 days, then the same piece of work will be done by 1 man, 1 woman and 1 boy in ______.


A
21 days
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B
24 days
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C
26 days
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D
33 days
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Solution

The correct option is B $$24$$ days
Let $$x$$ is the time it takes 1 man, 1 woman and 1 boy to do the piece of work 
One man works at the rate of $$\dfrac{1}{44}$$ of the piece of work per day
One women works at the rate of $$\dfrac{1}{2\times44}=\dfrac{1}{88}$$ of the piece of work per day
One boy works at the rate of $$\dfrac{1}{3\times44}=\dfrac{1}{132}$$ of the piece of work per day
So, to complete the piece of work we can write the equation as
$$\dfrac{1}{44}x+\dfrac{1}{88}x+\dfrac{1}{132}x=1$$   
$$\implies x=24$$
Therefore 1 man, 1 woman and 1 boy can do the same piece of work in $$24 $$days

Mathematics

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