Multiple choice

A person can complete a job in 91 days. He works alone on Day 1. On Day 2, he is joined by another person who also can complete the job in exactly 91 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?

  1. 12

  2. 15

  3. 13

  4. 14

  5. 11
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Each person completes 1/91 of job per day. Day 1: 1 person works = 1/91 completed. Day 2: 2 people work = 2/91 completed. Total after 2 days = 3/91. Day n: n people work. Total work = sum of (1+2+3+...+n)/91 = n(n+1)/(2×91). We need this = 1, so n(n+1) = 182. Testing n=13: 13×14 = 182. So 13 days needed. Option C (13) is correct.

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