CAT 2022 Slot 3 QA Q16 Time & Work

Question 16 of the Quantitative Ability (QA) section, CAT 2022 Slot 3, with CAT's official answer and a worked solution.

A group of \(N\) people worked on a project. They finished \(35 \%\) of the project by working 7 hours a day for 10 days. Thereafter, 10 people left the group and the remaining people finished the rest of the project in 14 days by working 10 hours a day. Then the value of \(N\) is
  1. A
    23
  2. B
    140
  3. C
    36
  4. D
    150

Answer: (B) 140 Time & Work MCQ

Solution

  1. Work in person-hours: \(N\cdot7\cdot10=70N\) did 35%, and \((N-10)\cdot14\cdot10=140(N-10)\) did 65%.
  2. \(\frac{70N}{35}=\frac{140(N-10)}{65}\Rightarrow 2N=\frac{28(N-10)}{13}\Rightarrow 26N=28N-280\).
  3. \(N=140\).

Shortcut. Plug options: \(N=140\) gives 9800 and 18200 person-hours, ratio 35:65.

Same concept in other years

See every question on Person-days or person-hours are proportional to work done.

More Time & Work questions from CAT

All 34 Time & Work questions asked since 2017.