Question

$X$ and $Y$ can do a piece of work in $30$ days. They work together for $6$ days and then $X$ quits and $Y$ finishes the work in $32$ more days. In how many days can $Y$ do the piece of work done?

• A. $30days$
• B. $32days$
• C. $10days$
• D. $40days$

Answer 1

Answer: (D)

$40days$

Let the total unit of work be $480$ units. (LCM of $30$ and $32$)
$X$ and $Y$ together complete the work in $30$ days.
$(X+Y)do=\frac{480}{30}=16units/day$
According to the question,
$16\times 6+Y\times 32=480$
$Y\times 32=384$
$Y=12$
$Y$ does $=12units/day$.
$Y$ alone can complete the work $=\frac{480}{12}=40days$.