Multiple choice

A, B and C can do a piece of work in 8 days. A and B can do the same piece of work in 10 days, whereas B and C can do the same piece of work in 12 days. How many days will A and C take to do the same piece of work?

  1. 10 days

  2. 12 days

  3. 14 days

  4. 15 days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let work be 1 unit. (A+B+C) = 1/8, (A+B) = 1/10, (B+C) = 1/12. We want (A+C). Note that (A+B) + (B+C) = A + 2B + C = 1/10 + 1/12 = 11/60. Also (A+B+C) = 1/8. So B = (A+B+C) - (A+C) is not direct. Instead, (A+B+C) - (B+C) = A = 1/8 - 1/12 = 1/24. (A+B+C) - (A+B) = C = 1/8 - 1/10 = 1/40. A+C = 1/24 + 1/40 = (5+3)/120 = 8/120 = 1/15. Thus, they take 15 days.

AI explanation

Let the total work be the least common multiple of 8, 10, and 12, which is 120 units. The one-day work of A plus B plus C is 15 units, A plus B is 12 units, and B plus C is 10 units. The one-day work of A alone is 15 minus 10, which is 5 units, and C alone is 15 minus 12, which is 3 units. The combined one-day work of A and C is 5 plus 3, giving 8 units, so they will complete the 120 units of work in 120 divided by 8 days, which equals 15 days.

Keep practicing — related questions