CAT 2024 Slot 1 · Quant · Question 5

Measure the work in hours rather than days. Renu needs 15\times 4=60 hours and Seema needs 8\times 5=40 hours.

So Renu completes \frac{1}{60} of the task per hour and Seema completes \frac{1}{40} per hour.

Renu works 2 hours a day, so Seema works double that, 4 hours a day.

Let Seema work for d days; then Renu works for 2d days.

Renu's total hours are 2d\times 2=4d, and Seema's total hours are d\times 4=4d — the same.

Together they finish the task: \frac{4d}{60}+\frac{4d}{40}=1.

Factoring, 4d\left( \frac{1}{60}+\frac{1}{40}\right)=4d\times \frac{5}{120}=\frac{d}{6}.

So \frac{d}{6}=1 and d=6 days.

Shortcut. The two conditions — Seema at double the hours per day, Renu for double the days — cancel exactly, so both put in the same number of hours. Spotting that turns the question into a single term.