Question

A can do a piece of work in 20 days whereas B can do it in 30 days. Both of them start the work together and work for sometime then B leaves. if A completes the remaining work in 10 days then find the number of days for which they worked together.

Answer 1

Method 1:

A and B can do the job in 30 and 20 days individually, so together they will take 30*20/(30 + 20) = 600/50 = 12 days.

The work that A can do in 5 days is 1/6th. So, A left when 5/6th of the work was done or A left after (5/6)*12 = 10 days

Total time taken = 10 + 5 = 15 days.

Method 2:

A and B can do the job in 30 and 20 days. A worked for the complete period of 'd' days, whereas B worked for 'd-5' days to finish the job

=> d/30 + (d-5)/20 = 1

=> 2d + 3d - 15 = 60

=> 5d = 75

=> d = 15 days

Hope this helps