CAT 2022 Slot 3 Question Paper - QA

Question 7

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

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.

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