Multiple choice

Three girls A, B and C can do a certain piece of work in 12, 36 and 48 days, respectively. All of them started working together and then B left after working for 2 days. After that A and C worked together for 3 days and then A left. In how many days was the remaining work done by C?

  1. 14

  2. 61/3

  3. 23/3

  4. 60/7

  5. 10
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A, B, and C work at rates of 1/12, 1/36, and 1/48 per day. In 2 days, they complete 2*(1/12 + 1/36 + 1/48) = 2*(12+4+3)/144 = 19/72. Then A and C work for 3 days, completing 3*(1/12 + 1/48) = 3*(5/48) = 15/48 = 5/16. The remaining work is 1 - (19/72 + 5/16) = 1 - (38+45)/144 = 1 - 83/144 = 61/144. C completes this at a rate of 1/48, taking (61/144) * 48 = 61/3 days.

AI explanation

Let the total work be 144 units, which is the least common multiple of 12, 36, and 48. The daily efficiencies of A, B, and C are 12, 4, and 3 units respectively. All three worked for 2 days to complete 38 units, and then A and C worked for 3 days to complete 45 units, leaving 61 units of work. C alone completes 3 units per day, so the time to finish the remaining 61 units is 61 divided by 3 days. The result is 61/3 days.

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