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Question 8 : 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?

  1. 16
  2. 22
  3. 20
  4. 18

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Explanatory Answer

Method of solving this CAT Question from Work and Time

Its given that B needs 25% more time than A
So, if Time taken by A = 4x days, Time taken by B = 5x days
A does half the work, So A works alone for 2x days --- (1)
A and B work for 4 days --- (2)
B works alone for \\frac{5𝑥}{20}) = \\frac{𝑥}{4}) days --- (3)

Total working days = 13
(1) + (2) + (3) = 13
2x + 4 + \\frac{𝑥}{4}) = 13 we get, x = 4
So, B alone can do the work in 5 × 4 = 20 days

The question is "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? B alone can finish the entire jon in 20 days"

Hence, the answer is 20 days

Choice C is the correct answer.

 

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