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Time and Work

A man and a b...

Question

A man and a boy working together can complete a work in 24 days, if for the last 6 days, the man alone does the work, then it is completed in 26 days, How long will the boy to complete the work alone ?

72 Days

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20 Days

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24 Days

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36 Days

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Solution

The correct option is A 72 Days
Let 1 man's 1 days' work = $\frac{1}{x}$ and 1 boy's 1 days' work = $\frac{1}{y}$ Then $\frac{1}{x} + \frac{1}{y} = \frac{1}{24}$
Also given $\frac{20}{x} + \frac{20}{y} + \frac{6}{x} = 1$ $\Rightarrow$ $20 (\frac{1}{x} + \frac{1}{y}) + \frac{6}{x} = 1 \Rightarrow 20 (\frac{1}{24}) + \frac{6}{x} = 1$
$\Rightarrow \frac{6}{x} = 1 - \frac{5}{6} \Rightarrow \frac{6}{x} = \frac{1}{6} \Rightarrow x = 36$ $∴$ $\frac{1}{y} = \frac{1}{24} - \frac{1}{36} = \frac{3 - 2}{72} = \frac{1}{72} \Rightarrow y = 72$
$∴$ The boy will take 72 days to complete the work alone

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A man and a boy working together can complete a work in 24 days, if for the last 6 days, the man alone does the work, then it is completed in 26 days, How long will the boy to complete the work alone ?

The correct option is A 72 DaysLet 1 man's 1 days' work = 1x and 1 boy's 1 days' work = 1y Then 1x+1y=124Also given 20x+20y+6x=1 ⇒ 20(1x+1y)+6x=1⇒20(124)+6x=1⇒6x=1−56⇒6x=16⇒x=36 ∴ 1y=124−136=3−272=172⇒y=72∴ The boy will take 72 days to complete the work alone