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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?

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72 Days

20 Days

24 Days

36 Days

answer is A.

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Detailed Solution

Given,
Complete a work by man and boy working together = 24 days
The man alone does the work in 6 days and complete the work = 26 days
Suppose that
A man works days = x
A boy works days = y
Thus,
1 man's 1 days' work

= \frac{1}{x}

1 boy's 1 days' work

= \frac{1}{y}

Now we have adding days of work then,

\frac{1}{x} + \frac{1}{y} = \frac{1}{24}

As per 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

Hence the boy will take 72 days to complete the work alone.
Option 1 is correct.

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