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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? [TITA]


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Explanatory Answer

Method of solving this CAT Question from Pipes and Cisterns

Given that 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.
Everyday a new person with the same efficiency joins the work
So by first day 1 person
Similarly by second day 2
Third day 3 and it goes on.......until it makes a total of 120
We have to find how many days are required to complete the job
So \\frac{15 × 16}{2}) = 120 [by \\frac{n(n+1)}{2})]
So 1 + 2 + 3 + 4 ...... till 15 days are required to complete this Job.
This will get completed in 15 days.
Hence 15 days are required to complete the job

The question is "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? [TITA]"

Hence, the answer is 15

 

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