Multiple choice

If A and B can finish a work in 10 days, B and C can finish the same work in 12 days, C and A can finish the same work in 15 days; then in how many days can A, B and C together finish half of the work?

  1. 8 days

  2. 5 days

  3. 4 days

  4. 3 days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the work be 60 units. A+B=6 units/day, B+C=5 units/day, C+A=4 units/day. Adding these gives 2(A+B+C) = 15 units/day, so A+B+C = 7.5 units/day. To finish half the work (30 units), they need 30 / 7.5 = 4 days.

AI explanation

Find the combined work rate of all three pairs by adding their one-day work amounts: (A+B) + (B+C) + (C+A) equals 1/10 + 1/12 + 1/15. This results in 2(A+B+C) = 1/4, meaning their combined daily work is 1/8. They complete the whole job in 8 days, so finishing half the work takes exactly 4 days.

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