Question

After a has finished 1/2 of a piece of work in 10 days b joins him for 5 days later a completes the work which still remains in 3 more days in how many days could b alone have done the complete work

Answer 1

A finished 1/2 or half the work in 10 days.
So 1 work will be completed by A in 20 days
In 1 day he does 1/20 part of the work.

Its given, A did 1/2 work in 10 days. Then B and A worked for 5 days. After that A alone worked for 3 more days to complete the work.

A in 1 day do: 1/20 work
A in 3 days did: 3/20 work.
Actual work remaining was 1/2. Out of this some was done by A&B together. And the remaining was done by A in 3 days which was 3/20 work.
Hence, 1/2 = (A&B)'s 5 days work + 3/20
A & B 5 days' work = 1/2 - 3/20 = 7/20 work
Let B in can complete a work in B days.
Hence in 1 day B does 1/B part of work.
In 5 days:
A did:5/20 work
B did: 5/B work
5/20 + 5/B = 7/20
5/B = 7/20 - 5/20 = 2/20 = 1/10
1/B = 1/50
Hence B in 1 day does 1/50 work.
So B alone can complete the whole work in 50 days.
Hope it helps.