Time Work

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. 20
  2. 16
  3. 22
  4. 18

Answer

Let the time taken by A to finish the job be a days.

Time taken by B to finish the job = 5a/4 days.

Let the job be of 100 units.

A works alone to finish 50 units of work. In the end, B works alone to finish 5 units of work.

Part of the job completed when A and B worked together for 4 days = 100 - 50 - 5 = 45

4(1/a + 4/5a) = 45

5a × 45 = 9 × 4

a = 4/25 

Time taken by B alone to complete the entire job = 5a/4 × 100 = 20 days.

The correct option is A.