Multiple choice

Directions: Solve the following question and mark the best possible option. Persons A and B can complete a job in 90 days and 150 days, respectively. A and B together work on day 1. On day 2, A and B are joined by two new persons with the equal efficiency. On the day 3, they are joined by two persons of equal efficiency. In the same pattern, every day, two new persons with the same respective efficiency join the work. How many days (approximately) are required to complete the job together?

  1. 20 days

  2. 5 days

  3. 10 days

  4. 18 days

  5. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A's rate = 1/90, B's rate = 1/150. Day 1: (1/90 + 1/150) = 8/450 = 4/225. Day 2: 2(A+B) = 8/225. Day 3: 3(A+B) = 12/225. Sum after n days = (A+B) * (1+2+...+n) = (4/225) * n(n+1)/2 = 1. n(n+1) = 225/2 = 112.5. n is approx 10.

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