CAT 2020 Slot 2 QA Question 3: John takes twice as much time as Jack to finish a job. Jack and Jim together take one-third of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John take

Question

John takes twice as much time as Jack to finish a job. Jack and Jim together take one-third of the time to finish the job than John takes working alone. Moreover, in order to finish the job, John take

Accepted Answer

Let Jack take $J$ days. Then John takes $2J$ days.

Jack and Jim together take one-third of John’s time, which is
$\dfrac{2J}{3}$
So their combined rate is
$\dfrac{3}{2J}$

Jack’s rate is
$\dfrac{1}{J}$
Therefore, Jim’s rate is
$\dfrac{3}{2J} - \dfrac{1}{J} = \dfrac{1}{2J}$
So Jim also takes $2J$ da