CAT 2024 Slot 2 QA Q6 Time & Work

Question 6 of the Quantitative Ability (QA) section, CAT 2024 Slot 2, with CAT's official answer and a worked solution.

Amal and Vimal together can complete a task in 150 days, while Vimal and Sunil together can complete the same task in 100 days. Amal starts working on the task and works for 75 days, then Vimal takes over and works for 135 days. Finally, Sunil takes over and completes the remaining task in 45 days. If Amal had started the task alone and worked on all days, Vimal had worked on every second day, and Sunil had worked on every third day, then the number of days required to complete the task would have been

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

Answer: 139 Time & Work TITA

Solution

  1. Let daily rates be \(a, v, s\). \(a+v = \frac{1}{150}\), \(v+s = \frac{1}{100}\), and \(75a + 135v + 45s = 1\).
  2. Rewrite: \(75(a+v) + 45(v+s) + 15v = 1 \Rightarrow \frac{1}{2} + \frac{9}{20} + 15v = 1 \Rightarrow v = \frac{1}{300}\).
  3. Then \(a = \frac{1}{300}\), \(s = \frac{2}{300}\). Take total work = 300 units: Amal 1, Vimal 1, Sunil 2 units per day.
  4. In each 6-day block: Amal 6, Vimal 3 (days 2, 4, 6), Sunil 2 days \(\times 2\) = 4, total 13 units.
  5. 23 blocks = 138 days give 299 units. Day 139 is the first day of a new block (only Amal works), adding 1 unit to finish 300.
  6. Answer: 139 days.

Same concept in other years

See every question on Work done in a repeating daily roster of workers.

More Time & Work questions from CAT

All 34 Time & Work questions asked since 2017.