CAT 2023 Slot 3 QA Question 12: Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish th

Question

Rahul, Rakshita and Gurmeet, working together, would have taken more than 7 days to finish a job. On the other hand, Rahul and Gurmeet, working together would have taken less than 15 days to finish th

Accepted Answer

Let Rakshita alone take r days. Let the combined work rate of Rahul and Gurmeet be s units per day.

From the actual work done,

$6\left(s + \dfrac{1}{r}\right) + 3\left(\dfrac{1}{r}\right) = 1$
$6s + \dfrac{9}{r} = 1$
$s = \dfrac{1 - \dfrac{9}{r}}{6}$

All three together take more than 7 days, so t