CAT 2019 Slot 1 QA Question & Solution
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?
Options
Solution
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