Time and work....?

Question

 

A takes 16 days and B takes 24 days to complete a piece of work. A alone worked for 4 days and B alone worked for 6 days. In how many days would they finish the remaining work together?

Answer 1

A can complete a piece of work in 16 days.

In one day A can complete 1/16 part of the work.

B can complete a piece of work in 24 days.

In one day B can complete 1/24 part of the work.

Work completed by A in 4 days = 4*(1/16) = 4/16 = 1/4 of the work.

Work completed by B in 6 days = 6*(1/24) = 6/24 = 1/4 of the work.

If both A and B work together, they can complete 1/4 +  1/4 = 2/4 = 1/2 nd part of the work.

Work completed by A and B together in 1 day = 1/16 + 1/24

= (3 + 2) / 48 = 5/48 of the work.

They can work in 48/5 days.

If 1/2 nd part of the work is completed by both of them, then the remaining half work can be completed in (1/2) * (48/5) days.

=  24/5 days

= 4.8 days.

Therefore in 24/5 or 4.8 days they would finish the remaining work together.