Multiple choice

A and B together can do a piece of work in 15 days while B and C together can do the same work in 12 days and C and A together can do the same work in 10 days. They all work together for 5 days, then B and C leave. How many more days will A take to finish the remaining work?

  1. 18

  2. 12

  3. 10

  4. 9

  5. 7
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A+B=1/15, B+C=1/12, C+A=1/10. 2(A+B+C) = 1/15 + 1/12 + 1/10 = (4+5+6)/60 = 15/60 = 1/4. A+B+C = 1/8. After 5 days, work done = 5/8. Remaining = 3/8. A's efficiency = (A+B+C) - (B+C) = 1/8 - 1/12 = (3-2)/24 = 1/24. Time for A = (3/8) / (1/24) = 9 days.

AI explanation

Using the combined work formula, the daily work rates are 1/15 for A and B, 1/12 for B and C, and 1/10 for C and A. Adding these gives 2 times the combined daily rate of A, B, and C as 1/4, meaning their combined daily rate is 1/8. Working together for 5 days, they complete 5/8 of the task, leaving 3/8 remaining. The individual daily work rate of A is the total rate minus the rate of B and C (1/8 minus 1/12), which equals 1/24. To finish the remaining 3/8 of the work at a rate of 1/24 per day, A requires 9 days.

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