A and B can do a piece of work in 45 and 40 days respectively. They began the work together but A leaves after some days and B finished the remaning work in 23 days. After how many days did A leave?

Question: A and B can do a piece of work in 45 and 40 days respectively. They began the work together but A leaves after some days and B finished the remaning work in 23 days. After how many days did A leave?

Solution:
Work done by B in 23 days {(1/40) × 23} = 23/40 part

Remaining work = (1 - 23/40) part
= 17/40 part

(A + B)'s 1 day's work = 1/45 + 1/40 = 17/360 part

Now,
17/360 part has done by (A + B) in 1 day
∴ 1 part has done by (A + B) in 360/17 day
∴ 17/40 part has done by (A + B) in {(360/17)(17/40)} days
= 9 days