X can do a piece of work in 40 days. He works at it for 8 days and then Y finishes it in 16 days. How long will they together take to complete the work?

40/3 days

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15 days

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20 days

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56 days

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None of these

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Solution

The correct option is A: $\frac{40}{3}$ days
Work done by X in 8 days = $(\frac{1}{40} \times 8) = \frac{1}{5}$
Remaining work = $(1 - \frac{1}{5}) = \frac{4}{5}$

Now, $\frac{4}{5}$ work is done by Y in $16$ days

Whole work will be done by Y in $(16 \times \frac{5}{4}) = 20$ days

$∴$ X's 1 day's work = $\frac{1}{40}$ , Y's 1 day's work = $\frac{1}{20}$ ,

(X + Y)'s 1 day's work = $(\frac{1}{40} + \frac{1}{20}) = \frac{3}{40}$

Hence, X and Y will together complete the work in $\frac{40}{3} = 13 \frac{1}{3}$ days

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