A and B can do a work in 45 and 40 days respectively. They began the work together, but A left after some time and B finishes the remaining work in 23 days. After how many days did A leave?

Explanation

A's `1` day work =`1/40`
B's `1` day work =`1/45`
A and B's `1` day work
=`1/40+1/45`
=`17/360`
A and B's `10` days work
=`(17/360) xx 10`
=`17/36`
Remaining work
=`1−17/36`
=`'36−17/36'`
=`'19/36'`
Now A can do `1` work in =`40` days.
He will do `19/36` work in
=`40 xx 19/36`
=`10 xx 19/9`
=`190/9`
=`21 1/9` days.