CAT 2022 Slot 3 QA Question & Solution
Question
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
Options
Solution
Let the unit of work done by 1 man in 1 hour and 1 day be 1 MDH unit (Man Day Hour).
Thus, in 7 hours per day for 10 days, the work done by N people =$N\times\ 7\times\ 10$ MDH units.
Since this is equal to 35% of the total work,
35% of the total work = $N\times\ 7\times\ 10$ MDH units.
Total work = $\frac{\left(N\times\ 100\times\ 7\times\ 10\right)}{35}=200\times N$ MDH units.
The work left = $200N-70N=130N$ MDH units.
Now, 10 people left the job. So, the number of people left = (N-10)
Since (N-10) people completed the rest of work in 14 days by working 10 hours a day,
$(N-10)\times\ 14\times\ 10=130N$
$10N=1400$
N = 140
Thus, the correct option is D.