NinetynineCAT 2024 Slot 1 QA Q5 Time & Work
Question 5 of the Quantitative Ability (QA) section, CAT 2024 Slot 1, with CAT's official answer and a worked solution.
Renu would take 15 days working 4 hours per day to complete a certain task whereas Seema would take 8 days working 5 hours per day to complete the same task. They decide to work together to complete this task. Seema agrees to work for double the number of hours per day as Renu, while Renu agrees to work for double the number of days as Seema. If Renu works 2 hours per day, then the number of days Seema will work, is
TITA: type in the answer. There are no options and no negative marking.
Answer: 6 Time & Work TITA
Solution
- Total work in hours: Renu needs \(15 \times 4 = 60\) hours, Seema \(8 \times 5 = 40\) hours. Take the work as \(120\) units: Renu does 2 units/hour, Seema 3 units/hour.
- Renu works 2 hours/day, so Seema works 4 hours/day. If Seema works \(d\) days, Renu works \(2d\) days.
- Work done: Renu \(2d \times 2 \times 2 = 8d\), Seema \(d \times 4 \times 3 = 12d\).
- \(8d + 12d = 120 \Rightarrow d = 6\).
Shortcut. Using LCM units (120) avoids fractions entirely.