Question

$X$ and $Y$ can do a piece of work in 30 days. $Y$ and $Z$ can do the same work in 20 days and $X$ and $Z$ can do the same in 24 days. Then, the number of days it will take to complete the work together by $X, Y$ and $Z$, is___

Answer 1

1-day work of $X$ and $Y=\frac{1}{30}$
1-day work of $\mathrm{Y}$ and $\mathrm{Z}=\frac{1}{20}$
1-day work of $X$ and $Z=\frac{1}{24}$
$2(x+y+z) =\frac{1}{30}+\frac{1}{20}+\frac{1}{24}=\frac{4+6+5}{120} a $
$ =\frac{15}{120}=\frac{1}{8}$
1-day work of $(x+y+z)=\frac{1}{8}$
So, the required time is 8 days