Quantitative Aptitude – Arithmetic – Time and Work – When they work alone, B needs 25%

Slot -1 – Quantitative Aptitude – Arithmetic – Time and Work – When they work alone, B needs 25%

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?

a) 22
b) 18
c) 20
d) 16

Solution:
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
correct answer c) 20

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