A and B can do a piece of work in 28 days and 35 days respectively. They began to work together but A leaves after some time and B completed the remaining work in 17 days. After how many days did A leave?

Question: A and B can do a piece of work in 28 days and 35 days respectively. They began to work together but A leaves after some time and B completed the remaining work in 17 days. After how many days did A leave?

Solution:
Work done by B in 17 days (1/35) × 17 = 17/35 part

Remaining work = 1 - 17/35 = 18/35

(A + B)'s 1 day's work = 1/28 + 1/35 = 9/140 part

Now, 9/140 work has done by (A + B) in 1 day
So, 18/35 work has done by (A + B) in (140/9) × (18/35) days
= 8 days