Multiple choice

A and B together can do a piece of work in 80 days. B and C can do it in 120 days. On the first day, only A and B worked together and on the second day, only B and C worked together. For the following days, B worked for all the days, but A and C worked on alternate days only. How long did the work last?

  1. 88 days

  2. 90 days

  3. 96 days

  4. 98 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

A+B = 1/80, B+C = 1/120. Let B's rate be b. A = 1/80 - b, C = 1/120 - b. Day 1: A+B = 1/80. Day 2: B+C = 1/120. Day 3: A+B = 1/80. Day 4: B+C = 1/120. In 2 days, work done = 1/80 + 1/120 = 5/240 = 1/48. Total work = 1. Days = 1 / (1/96) = 96 days.

AI explanation

Let the one day work of A, B and C be a, b and c. The pattern of work for every two days is (a + b) + (b + c), which gives 1/80 + 1/120 = 5/240 = 1/48 of the work. This means the work is completed in 48 cycles of 2 days, resulting in a total of 96 days.

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