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The question below is from previous year CAT question from CAT 2018 exam comes from CAT Time and Work: When they work alone, B needs 25% . Find out by answering this question which tests an aspirant’s Quantitative Ability Skills:
Q. 4: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?
ratio of time taken by A and B to complete the work alone = 1: 1.25 = 4x : 5x
As A complete half of the work alone and B complete 5% of the work alone, so they will complete remaining 45% of work in 4 days .
So time taken by them to complete the whole work together = 4 * 100/45 = 80/9
Or (4x*5x)/(4x+5x) = 80/9
x = 4
Thus time taken by B to complete the work alone = 5x = 20 days