Multiple choice

A, B and C together can finish a work in 10 days. A alone can do it in 24 days while B can do it in 30 days. A and B work together for 12 days and leave the rest of the work to be completed by C. How many days will C take to do the rest of the work?

  1. 4

  2. 6

  3. 8

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Work rates: A+B+C = 1/10, A = 1/24, B = 1/30. C = 1/10 - (1/24 + 1/30) = 1/10 - (5+4)/120 = 1/10 - 9/120 = 12/120 - 9/120 = 3/120 = 1/40. A+B work for 12 days: (1/24 + 1/30) * 12 = (9/120) * 12 = 9/10. Remaining work = 1/10. C takes (1/10) / (1/40) = 4 days.

AI explanation

Using the least common multiple method, let the total work be 120 units. The combined rate of A, B, and C is 12 units per day, A's rate is 5 units per day, and B's rate is 4 units per day, meaning C's rate is 12 minus 5 minus 4, or 3 units per day. A and B working together for 12 days complete 12 times 9 units, which is 108 units. The remaining work is 120 minus 108, equaling 12 units. C will complete these 12 remaining units at a rate of 3 units per day, taking 4 days.

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