#Time & Work - 3

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally, B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?
1) 22
2) 18
3) 20
4) 16

Solution-

Let A does 5x units/day
B does 4x units/day
Let total work = 100%
A does 50% of work alone and B does 5% work alone
Remaining Work = 100 - (50+5) = 45%
This 45% = 4*(4x+5x)
=> 4x = 5%
=>80x = 100%
B will take, 80x/4x = 20 days Ans

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