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CAT 2017 [slot 1] Question with solution 02

Question 2:
A person can complete a job in 120 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 120 days. On Day 3, they are joined by another person of equal efficiency. Like this, everyday a new person with the same efficiency joins the work. How many days are required to complete the job?
Answer: 15

Let the rate of work of a person be x units/day. Hence, the total work = 120x.

It is given that one first day, one person works, on the second day two people work and so on.

Hence, the work done on day 1, day 2,... will be x, 2x, 3x, ... respectively.

The sum should be equal to 120x.

$120x = x× \frac{n(n+1)}{2}$

$n^2 + n - 240 = 0$

n = 15 is the only positive solution.

Hence, it takes 15 days to complete the work.

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