Question

X is twice as fast as Y and hence takes 30 days less than Y to complete a job. Find the time taken by X and Y together to complete it.

Answer 1

Given $X$ is twice as fast as $Y$

$\therefore$ if $X$ takes ${}^{\prime }{a}^{\prime }$ days to complete the work

then $Y$ will take ${}^{\prime }2s^{\prime }$ days to complete same work

Given, $2a-a=30$

$\Rightarrow a=30$

$\therefore$ $X$ takes $30$ days and $Y$ takes $60$ days to complete the same work

Say we have $60$ units of work.

Then in $1$ day $X$ will do $2$ units of work

where as $Y$ will do $1$ units of work

$\therefore$ if they work together then in $1$ day they will complete $3$ units of work.

$\therefore$ To complete $60$ units of work they would need $\frac{60}{3}=20$ days

$\therefore$ $X$ & $Y$ together can complete a work in $20$ days.