Question

A and B can do a piece of work in 45 days and 40 days respectively. They began to do the work together but A leaves after some days and then B completed the remaining work in 23 days.

The number of days after which A left the work was ?

Answer 1

Productivity of A= 1/45 work/day
Productivity of B = 1/40 work/day
Productivity of Both together = 1/45 +1/40
= 17/360 per day.

B did 23 days of work, ie., 23*1/40 = 23/40 amount of work.
Remaining work = 1 - 23/40 = 17/40.
This is done by A & B together.
Number of days they worked together = (17/40) / (17/360)
= 9

Answer 2

(A+B)’s 1 day’s work =[1/45+1/40]=17

=>Work done by B in 23 days=1×23/40=23/40
=>Remaining work =1−23/40=17/40

=>Now, 17/360 work was done by (A+B) in 1 day

=>17/40 work was done by (A+B) in 1×360/17×17/40=9 days
therefore A left after 9 days