Multiple choice

In the given questions, two quantities are given, one as Quantity I and another as Quantity II. You have to determine relationship between two quantities and choose the appropriate option. B is thrice as efficient as C. B and C can compete a work together in 45/2 days. A takes 50% more days than the days taken by A and B to complete the same work together. Quantity 1: No. of days taken by fastest among them to complete the work alone. Quantity 2: Time taken by A and C to complete the work together.

  1. Quantity I > Quantity II

  2. Quantity I < Quantity II

  3. Quantity I ≥ Quantity II

  4. Quantity I ≤ Quantity II

  5. Quantity I = Quantity II or No relation.
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A Correct answer
AI explanation

Let the efficiencies of B and C be 3 and 1, giving a combined efficiency of 4. The total work is 4 multiplied by 45/2, which equals 90. Since A takes 50 percent more days than A and B together, the combined efficiency of A and B is 2 divided by 3, meaning the total efficiency of A, B, and C is 3 plus 2/3, or 11/3. Solving gives A's efficiency as 2/3, so A takes 135 days, B takes 30 days, and C takes 90 days. Quantity 1 for the fastest worker B is 30 days, while Quantity 2 for A and C working together is 90 divided by 11/3, which is about 24.5 days. Therefore, Quantity I is greater than Quantity II.

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