$\frac{2}{5}$ of a work is distributed among 5 workers equally such that each worker gets $\frac{1}{5} th$ . One of them further decided to give his entire work to 5 workers equally such that each worker gets $\frac{1}{5} th$ . What is the fraction of work alloted to each worker?

\frac{1}{125}

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\frac{6}{125}

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\frac{4}{125}

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\frac{2}{125}

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Solution

The correct option is D $\frac{2}{125}$
Total work = $\frac{2}{5}$
One person got $\frac{1}{5} th$ of it.
So, the amount of work given to each person is:
$\frac{1}{5} of \frac{2}{5} = \frac{1}{5} \times \frac{2}{5} = \frac{1 \times 2}{5 \times 5} = \frac{2}{25}$
Now, one of the workers distributed his/her work to two workers such that each one got $\frac{1}{5} .$
So, the amount of work given to each worker is:
$\frac{1}{5} of \frac{2}{25} = \frac{1}{5} \times \frac{2}{25} = \frac{1 \times 2}{5 \times 25} = \frac{2}{125}$

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