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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?

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? Correct Answer 20

Calculation:

Let number of days taken by A alone to complete job be a days.

Number of days taken by alone B to complete job = a × 125/100 = 5a/4

Number of days A worked to complete half of work = 1/2 × a = a/2

A's 1 day's work = 1/a

B's 1 day's work = 4/5a

Ratio of time taken alone by A and B = 4 : 5

(A + B)'s 1 days work = 1/a + 4/5a = 9/5a

45% of work is completed in 4 days by A and B.

If they work together, then work will complete in = 4 × 100/45 = 80/9

⇒ 9/5a = 9/80

⇒ a = 16

∴ Number of days in which B alone can complete work = 16 × 5/4 = 20 days

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