Question

It takes $8,12$ and $16$ days for $X,Y$ and $Z$ respectively to complete a work. If $X$ works on it for $2$ days and then $Y$ works on it for until $25\%$ of the work is left for $Z$ to do, how many days it takes to complete the work?

• A. $10$ days
• B. $12$ days
• C. $8$ days
• D. $14$ days

Answer 1

The correct option is B $12$ days

$X$ does the work in $8$ days.

$\therefore$ In $1$ day $X$ does $\frac{1}{8}$ work,

$Y$ does the work in $12$ days.

$\therefore$ In $1$ day $Y$ does $\frac{1}{12}$ work and

$Z$ does the work in $16$ days.

$\therefore$ In $1$ day $Z$ does $\frac{1}{16}$ work.

So, In $2$ days, $X$ does $2\times \frac{1}{8}$ work $=\frac{1}{4}$work,

Now the work left after $Y$ leaves$=25\%$ work $=\frac{1}{4}$ work

This is done by $Z$ in $\frac{1}{4}\times 16$ days $=4$ days.

So $Y$'s share of work $=(1-\frac{1}{4}-\frac{1}{4})$ work $=\frac{1}{2}$ work.

This work he will do in $\frac{1}{2}\times 12$ days $=6$ days.

$\therefore$ The total number of days required to finish the work

$=(2+6+4)$ days $=12$ days.

Ans- Option $B$.