A and B can do a piece of work in 45 and 40 days respectively. they began the work together, but A leaves after same days and B finished the remaining work in 23 days. after how many did A leave.

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As per question given in paragraph:

A alone complete the work in = 45 days.

B alone complete the work= 40 days

Work of A =1/45

Work of B=1/40

Because time and work are inverse proportionate.

Total work= 1/45+1/40=

360units( take LCM of both the work)A make 360*1/45= 8 unit/day

B make360*1/40= 9 units/day

According to question A leaves the job after some day and remaining work is done by B alone in 23 days.

So work of B after A leaves= 23 days*9 units/day= 207 units

Work done

by(A+B)= 360-207= 153 unitsA+B can make together (8+9)= 17 units per day.

So the time after A leaves or he had worked together with

B=153/17units=9daysHence A leaves his job after 9 days.