Multiple choice

If $A$ and $B$ can do a piece of work in $15$ days, $B$ and $C$ can do the same work in $20$ days and $A$ and $C$ can do ti in $30$ days, then $A$ alone can do the work in

  1. $30$ days
  2. $40$ days
  3. $45$ days
  4. $50$ days
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rates: A+B=1/15, B+C=1/20, A+C=1/30. Summing: 2(A+B+C) = 1/15 + 1/20 + 1/30 = (4+3+2)/60 = 9/60 = 3/20. So A+B+C = 3/40. A = (A+B+C) - (B+C) = 3/40 - 1/20 = 1/40. A takes 40 days.

AI explanation

Let the total work be the Least Common Multiple of 15, 20, and 30, which is 60 units, making the daily capacities 4 units for A and B, 3 units for B and C, and 2 units for A and C. Adding these three equations gives 2A + 2B + 2C = 9 units, so the combined daily capacity of A, B, and C is 4.5 units, meaning A and C together work at 0.5 units per day. Subtracting the combined rate of A and C from the total capacity of all three yields A's daily capacity as 4 units, meaning A alone will finish the 60 units in 40 days.

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