Multiple choice

A, B and C can complete a work in 10, 12 and 15 days, respectively. All three of them start together; but after two days, A leaves the job. Also, B leaves the job 3 days before the work is completed. C completes the remaining work alone. In how many days is the total work completed?

  1. 5

  2. 6

  3. 7

  4. 8
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let total days be T. A works 2 days (2/10), B works (T-3) days (T-3)/12, C works T days (T/15). 2/10 + (T-3)/12 + T/15 = 1. Multiply by 60: 12 + 5(T-3) + 4T = 60. 12 + 5T - 15 + 4T = 60. 9T - 3 = 60. 9T = 63. T = 7.

AI explanation

Assume the total work is the least common multiple of 10, 12, and 15, which is 60 units, making their daily work units 6, 5, and 4 respectively. Since A works for only 2 days, A completes 12 units, leaving 48 units of work to be completed by B and C. Let D be the total number of days taken from the start to the finish; since B leaves 3 days before the work is completed, B works for D minus 3 days, while C works for all D days. The equation for the remaining work is 5 multiplied by D minus 3, plus 4 multiplied by D, which equals 48 units. Solving 9D minus 15 equals 48 gives D equals 7 days.

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