Question

$\frac{2}{3}$ of a work is distributed among 4 people equally such that each one gets $\frac{1}{4}\mathrm{th}$ of it. One of them further decides to give his work to 2 workers equally such that each worker gets $\frac{1}{2}\mathrm{th\; of\; the\; work.}$ What is the fraction of work alloted to each worker?

• A. $\frac{1}{15}$
• B. $\frac{1}{9}$
• C. $\frac{1}{6}$
• D. $\frac{1}{12}$

Answer 1

The correct option is D $\frac{1}{12}$

Total work = $\frac{2}{3}$
Each person gets $\frac{1}{4}\mathrm{th}$ of it.
So, the amount of work given to one person is:
$\frac{1}{4}\mathrm{of}\frac{2}{3}=\frac{1}{4}\times \frac{2}{3}=\frac{1\times 2}{4\times 3}=\frac{1\times 2}{2\times 2\times 3}=\frac{1}{2\times 3}=\frac{1}{6}$
Now, one of the persons distributed his/her work to two workers such that each one gets $\frac{1}{2}.$
So, the amount of work given to each worker is:
$\frac{1}{2}\mathrm{of}\frac{1}{6}=\frac{1}{2}\times \frac{1}{6}=\frac{1\times 1}{2\times 6}=\frac{1}{12}$