CAT 2023 Slot 3 QA Q16 Time & Work

Question 16 of the Quantitative Ability (QA) section, CAT 2023 Slot 3, with CAT's official answer and a worked solution.

Gautam and Suhani, working together, can finish a job in 20 days. If Gautam does only 60% of his usual work on a day, Suhani must do 150% of her usual work on that day to exactly make up for it. Then, the number of days required by the faster worker to complete the job working alone is

TITA: type in the answer. There are no options and no negative marking.

Answer: 36 Time & Work TITA

Solution

Gautam's lost 40% equals Suhani's extra 50%: \(0.4G = 0.5S \Rightarrow G:S = 5:4\).
\(G+S = \frac1{20}\), so \(G = \frac59\cdot\frac1{20} = \frac1{36}\) and \(S=\frac1{45}\).
The faster worker, Gautam, takes 36 days.