NinetynineCAT 2022 Slot 2 QA Q2 Time & Work
Question 2 of the Quantitative Ability (QA) section, CAT 2022 Slot 2, with CAT's official answer and a worked solution.
Working alone, the times taken by Anu, Tanu and Manu to complete any job are in the ratio 5 : 8 : 10. They accept a job which they can finish in 4 days if they all work together for 8 hours per day. However, Anu and Tanu work together for the first 6 days, working 6 hours 40 minutes per day. Then, the number of hours that Manu will take to complete the remaining job working alone is
TITA: type in the answer. There are no options and no negative marking.
Answer: 6 Time & Work TITA
Solution
- Times are 5 : 8 : 10, so hourly rates are \(\frac15:\frac18:\frac1{10} = 8:5:4\) units.
- All three take \(4\times8=32\) hours, so the job is \(17\times32=544\) units.
- Anu and Tanu work \(6\times 6\frac23=40\) hours at 13 units/hour, doing 520 units.
- The remaining 24 units at Manu's 4 units/hour take 6 hours.