Tried this work and time question from Cat 2022 slot 3 but got confused after setting up the equation. Can someone check?

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 
A. 23
B. 140
C. 36
D. 150

Shruti T · Accepted Answer

This is a work and time problem where setting up man-hours correctly is key. First, N people worked 7 hours a day for 10 days and completed 35% of the work. That means each person worked 70 hours (7&times;10), so total effort = N &times; 70 hours, which equals 35% of the work. Now scale it up: if N people do 35% of the work in N&times;70 man-hours, then 1% of the work = N&times;2 hours. So the full project would need N&times;200 man-hours.
That means the remaining 65% of the work needs N&times;130 man-hours. But now only (N&ndash;10) people are working for 14 days, 10 hours daily &mdash; so they work 140 hours each. Total effort = (N&ndash;10) &times; 140 hours. That also equals 65% of the work. So now set up the equation: N &times; 130 = (N&ndash;10) &times; 140 Solve this to get 13N = 14N &ndash; 140
N = 140
So the correct answer is Option B.

Jayant M · Answer

Once you break the project into man-hours, the equation becomes easier to manage.

N people work 7 hrs/day for 10 days,  total = N &times; 70 hrs
That&rsquo;s 35% of the project
Remaining 65% is done by (N&ndash;10) people working 14 days, 10 hrs/day,  each does 140 hrs
So remaining effort = (N&ndash;10) &times; 140 hrs
Equate the two: N &times; 130 = (N&ndash;10) &times; 140
Solve the equation: 13N = 14N &ndash; 140 ,  N = 140.

So the value of N is 140, and the answer is Option B. Just keep each step in terms of total hours worked per person and match them using work percentages.