Multiple choice

A and B complete a piece of work in $24$ days. B and C do the same work in $36$ days; and A and B and C together finish it in $18$ days. In how many days will A and C together complete the work ?

  1. $24$ days
  2. $20$ days
  3. $14$ days
  4. $22$ days
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let total work be 72 units. A+B = 3 units/day, B+C = 2 units/day, A+B+C = 4 units/day. C = (A+B+C) - (A+B) = 4 - 3 = 1 unit/day. A = (A+B+C) - (B+C) = 4 - 2 = 2 units/day. A+C = 2 + 1 = 3 units/day. Time = 72 / 3 = 24 days.

AI explanation

Given (A+B)'s work is 1/24, (B+C)'s is 1/36, and (A+B+C)'s is 1/18. C's 1 day work is (1/18 - 1/24) = 1/72. A's 1 day work is (1/18 - 1/36) = 1/36. (A+C)'s 1 day work is (1/36 + 1/72) = 3/72 = 1/24. A and C together will complete the work in 24 days.

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