Multiple choice

A and B can do a piece of work in $40$ days, B and C in $30$ days, and C and A in $24$ days. In what time can each of them finish it by working alone?

  1. A in $20$ days, B in $150$ days, C in $20$ days
  2. A in $30$ days, B in $130$ days, C in $30$ days
  3. A in $60$ days, B in $120$ days, C in $40$ days
  4. A in $50$ days, B in $130$ days, C in $20$ days
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let rates be a, b, c. 1/a + 1/b = 1/40, 1/b + 1/c = 1/30, 1/c + 1/a = 1/24. Summing gives 2(1/a + 1/b + 1/c) = 1/40 + 1/30 + 1/24 = (3+4+5)/120 = 12/120 = 1/10. So 1/a + 1/b + 1/c = 1/20. Then 1/c = 1/20 - 1/40 = 1/40 (C=40), 1/a = 1/20 - 1/30 = 1/60 (A=60), 1/b = 1/20 - 1/24 = 1/120 (B=120).

AI explanation

Given 1/40 + 1/30 + 1/24 for the combined pairs, A+B+C's 1 day work is (1/2)(1/40 + 1/30 + 1/24) = 1/2 * 1/10 = 1/20. C's 1 day work is (1/20 - 1/40) = 1/40, so C takes 40 days. A's 1 day work is (1/20 - 1/30) = 1/60, so A takes 60 days. B's 1 day work is (1/20 - 1/24) = 1/120, so B takes 120 days. The result is A in 60 days, B in 120 days, C in 40 days.

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