CAT 2018 Question Paper Shift 1 Solved Paper

Question : 74 of 100

Marks: +1, -0

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? Options

Validate

Solution:

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

{B}

to finish the job

=\;{5}/{4} a

days.
Part of the job completed when

{A}

and

{B}

worked together for 4 days

=1=\;{1}/{2}-\;{5}/{100}=\;{9}/{20}

4(\;{1}/{a}+\;{1}/{{5 a}/{4}})=\;{9}/{20} ⇒ a=16

Time taken by

{B}

alone to complete the entire job

=5 {a} {/} 4=20

days.

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