CAT 2018 Quant Questions

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?

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Correct Answer: 1
Let the time taken by A to finish the job be “a” days.
Time taken by B to finish the job $=\frac{5}{4} a$ days.
Part of the job completed when A and B worked together for 4 days = $1=\frac{1}{2}-\frac{5}{100}=\frac{9}{20}$
$4\left(\frac{1}{a}+\frac{1}{\frac{5 a}{4}}\right)=\frac{9}{20} \Rightarrow a=16$
Time taken by B alone to complete the entire job = 5a/4 = 20 days.

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