Question

A alone can do a piece of work in 12 days and B alone do the same work 15 days. A works alone for 4 days . In how many days will A and B together finish the remaining work.

Answer 1

A alone can do the work in 12 days he can do = 1/12 work in one day

B alone can do the work in 15 days
He can do = 1/15 work in one day

A works for 4 days
Work done = 4 × 1/12 = 4/12 = 1/3
work remaining = 1 - 1/3 = 2/3

A and B together can do = 1/12 + 1/15 = (5+4)/60 = 9/60 work in 1 day.

To finish the remaining work together, they need = (2/3) ÷ (9/60) = 2/3 × 60/9 = 40/9 days = 4 4/9 days

They need 4 4/9 days to finish the work.

Answer 2

Days required by A to do a

piece of work = 12 days =1/12days

Days required by B to do a

piece of work = 15 days =1/15 days

Total work = 1/12 + 1/15

= 9/60 days

No. Of days A works alone = 4 days = 1/4days

Therefore, A and B work together in:

= 1/4 - 9/60

= 6/60 days

= 1/10 days

Therefore, A and B work together in:1 ÷ 1/10 days = 10 days