cat 2019 Question 20

Question

At their usual efficiency levels, A and B together finish a task in 12 days. If A had worked half as efficiently as she usually does, and B had worked thrice as efficiently as he usually does, the task would have been completed in 9 days. How many days would A take to finish the task if she works alone at her usual efficiency?

Accepted Answer

Assuming A completes a units of work in a day and B completes B units of work in a day and the total work = 1 unit

Hence, 12(a+b)=1.........(1)

Also, 9($\ \frac{\ a}{2}$+3b)=1 .........(2)

Using both equations, we get, 12(a+b)= 9($\ \frac{\ a}{2}$+3b)

=> 4a+4b=$\ \frac{\ 3a}{2}$+9b

=> $\ \frac{\ 5a}{2}$=5b

=> a=2b

Substituting the value of b in equation (1),

12($\ \frac{\ 3a}{2}$)=1

=> a=$\ \frac{\ 1}{18}$

Hence, the number of days required = 1/($\ \frac{\ 1}{18}$)=18

Question 20.

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Question 20.

Question Explanation

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