Mamun and Shahin can do a piece of work in 21 and 24 days respectively. They started the work together and after some days Mamun leaves the work and Shahin completes the remaining work in 9 days. After how many days did Mamun leave?

Question: Mamun and Shahin can do a piece of work in 21 and 24 days respectively. They started the work together and after some days Mamun leaves the work and Shahin completes the remaining work in 9 days. After how many days did Mamun leave?

Solution:
Mamun can do 1/21 work in 1 day

Shahin can do 1/24 work in 1 day
in 9 days, Shahin does 9/24 work
= 3/8 work
remaining work 1 - (3/8)
= (8 - 3)/8
= 5/8 work, which is completed by both.

They both can do (1/21) + (1/24)
= (8 + 7)/168
= 15/168 work

15/168 work is done in 1 day
5/8 work is done (168 × 5)/(15 × 8)
= 7 days