Multiple choice

$A$ does half as much work as $B$ and $C$ does half as much work as $A$ and $B$ together in the same time. If $C$ alone can do the work in $40$ days, all of them together will finish the work in

  1. $13$ days
  2. $15$ days
  3. $20$ days
  4. $13.33$ days
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Let work rates be A, B, C. A = 0.5B, C = 0.5(A+B) = 0.5(1.5B) = 0.75B. Given C = 1/40, then 0.75B = 1/40, so B = 1/30. Then A = 1/60. Total rate = 1/60 + 1/30 + 1/40 = (2+4+3)/120 = 9/120 = 3/40. Time = 40/3 = 13.33 days.

AI explanation

Let the work rates of A, B and C be a, b and c, so the given conditions mean a equals half of b, making the ratio of a to b equal to 1 to 2, and c equals half of the sum of a and b. Therefore, c equals half of 3 parts, giving individual rate ratios of a to b to c as 2 to 4 to 3. Since C takes 40 days, their combined daily rate is 9 parts divided by 40, meaning they complete 1 work in 40 divided by 9 days, which is approximately 13.33 days.

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