Multiple choice

Three engineers A, B and C take up an assignment from a company. A and B together can complete this assignment in 6 days, B and C together can complete it in 12 days, while A and C together can complete it in 3 days. What will be the number of days taken by C to complete the assignment working alone?

  1. 3

  2. 4

  3. 6

  4. 8

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

A+B = 1/6, B+C = 1/12, A+C = 1/3. Summing these: 2(A+B+C) = 1/6 + 1/12 + 4/12 = 7/12. A+B+C = 7/24. C = (A+B+C) - (A+B) = 7/24 - 4/24 = 3/24 = 1/8. So C takes 8 days.

AI explanation

Let the total work be 12 units. The efficiencies for A and B together, B and C together, and A and C together are 2, 1, and 4 units per day respectively. Adding these three equations gives 2 multiplied by the sum of A, B, and C equals 7 units per day, so their combined efficiency is 3.5 units per day. C's efficiency is the combined rate minus the rate of A and B, which is 3.5 minus 2, equaling 1.5 units per day. The time taken by C alone is 12 divided by 1.5, which equals 8 days.

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