Multiple choice

Passage

Given below are two quantities named A and B. Based on the given information, you have to determine the relation between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Quantity A: A boy can do homework in 2 hours. The number of home-works he can complete if he works for 6 hrs. Quantity B: A can do a piece of work in 20 days. B can do the same work in 25 days. A and B work together for 9 days. C who can do the same work in 10 days joins them now. Then the number of days in which the remaining work will be completed?

  1. Quantity A > Quantity B

  2. Quantity A < Quantity B

  3. Quantity A ≥ Quantity B

  4. Quantity A ≤ Quantity B

  5. Quantity A = Quantity B or relationship cannot be determined.
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A Correct answer
Explanation

Quantity A: In 6 hours, completing homework at 2 hours per assignment gives 3 homework assignments. Quantity B: A's work rate is 1/20 per day, B's is 1/25 per day, and C's is 1/10 per day. A and B together for 9 days complete (1/20 + 1/25) × 9 = 9/20 + 9/25 = 81/100 of the work. The remaining 19/100 is completed by all three working at combined rate 1/20 + 1/25 + 1/10 = 34/100 per day, taking 19/34 ≈ 0.56 days. Since 3 > 0.56, Quantity A > Quantity B.

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