CAT 2018 Quant Questions

Question:
When they work alone, B needs 25% more time to ?nish a job than A does. They two ?nish 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 ?nally B works alone to complete the remaining 5% of the job. In how many days can B alone ?nish the entire job?

20
16
22
18
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Correct Answer: 1

Let us assume that A can complete 'a' units of work in a day and B can complete 'b' units of work in a day. 

A works alone till half the work is completed. 

A and B work together for 4 days and B works alone to complete the last 5% of the work. 

=> A and B in 4 days can complete 45% of the work.

Let us assume the total amount of work to be done to be 100 units.

4a + 4b = 45 ---------(1)

B needs 25% more time than A to finish a job. 

=> 1.25*b = a ----------(2)

Substituting (2) in (1), we get, 

5b+4b = 45

9b = 45

b = 5 units/day

B alone can finish the job in 100/5 = 20 days. 

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CAT 2018 Quant Questions
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