M and N can do a piece of work in 20 days and 12 days respectively. M started the work alone and then after 4 days, N joined him till the completion of the work. How long did the work last?

Question: M and N can do a piece of work in 20 days and 12 days respectively. M started the work alone and then after 4 days, N joined him till the completion of the work. How long did the work last?

Solution:
work done by m in 4 days = (1/20) × 4 = 1/5
∴ Remaining work = 1 - (1/5) = 4/5

(M + N)'s 1day's work = (1/20) + (1/12)
= 8/60 = 2/15

Now, 2/15 work is done by M and N in 1 day.
So, 4/5 work will be done by M and N in = (15/2) × (4/5)
= 6 days

∴ Total time taken = (6 + 4) days = 10 days