Multiple choice

𝐴, 𝐡 and 𝐢 together can complete a certain work in 10 days. If 𝐴's efficiency is decreased by 20%, 𝐡's efficiency is increased by 20% whereas 𝐢 works at his usual efficiency, it still takes them 10 days to complete the work. However, if 𝐴 works at his usual efficiency, 𝐡 increases his efficiency by 50% whereas 𝐢 increases his efficiency by 25%, then in how many days can they together complete the work (in days).

  1. 6

  2. 8

  3. 12

  4. Cannot be determined
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let efficiencies be A, B, C. From the first condition, A+B+C = 1/10. From the second, 0.8A + 1.2B + C = 1/10. Subtracting gives 0.2A = 0.2B, so A = B. Substituting back, 2A + C = 1/10. The third case asks for time with A, 1.5B, 1.25C. Since A=B, this is A + 1.5A + 1.25C = 2.5A + 1.25C = 1.25(2A + C) = 1.25(1/10) = 1/8. Time = 8 days.

AI explanation

Let the efficiencies of A and B be 5x and 5y. The first condition states 4x plus 6y plus the efficiency of C equals 5x plus 5y plus the efficiency of C, which simplifies to y equals x. Since their combined efficiency is 1/10 of the work per day, the second condition has A working at 5x, B at 7.5x, and C at 1.25 of his normal rate. The total work equation becomes 5x plus 5y plus 5z equals 1, and since y equals x, we have 10x plus 5z equals 1. The new combined rate is 5x plus 7.5x plus 1.25z, which equals 12.5x plus 1.25z, or 1.25 multiplied by (10x plus 5z). Substituting 1 for the term in parentheses gives a new rate of 1.25 divided by 10, which is 1/8 of the work per day. Therefore, they will complete the work in 8 days. The correct answer is 8.

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