Multiple choice

$A$ is $50\%$ as efficient as $B$. $C$ does half of the work done by $A$ and $B$ together. If $C$ alone does the work in $40$ days, then $A, B$ and $C$ together can do the work in

  1. $\displaystyle 13\frac{1}{3}$ days
  2. $15$ days
  3. $20$ days
  4. $30$ days
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A Correct answer
Explanation

A = 0.5B. C = 0.5(A+B) = 0.5(1.5B) = 0.75B. C does work in 40 days, so total work = 40 * 0.75B = 30B. A+B+C = 0.5B + B + 0.75B = 2.25B. Time = 30B / 2.25B = 30 / 2.25 = 13.33 days.

AI explanation

Since A is 50 percent as efficient as B, the ratio of their work is 1 to 2, giving a combined daily work rate of 3 units for A and B. The problem states C does half the work done by A and B together, meaning C's daily work rate is 3 divided by 2, which equals 1.5 units. Because C alone takes 40 days, the total work is 1.5 multiplied by 40, which equals 60 units. Adding the daily work rates of A, B, and C gives 3 plus 1.5, totaling 4.5 units per day. Dividing the total work of 60 units by their combined daily rate of 4.5 units gives the time required as 13 and 1/3 days.

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