Multiple choice

Directions: In the given question, two quantities are given, one as 'Quantity 1' and another as 'Quantity 2'. You have to determine the relationship between the two quantities and choose the appropriate option. Four persons A, B, C and D together can complete a job in 40/7 days and the ratio of the efficiencies of A, B, C and D is 8 : 4 : 6 : 3. Quantity 1: Time taken by A and B to complete the job together Quantity 2: Time taken by C and D to complete the job together

  1. Quantity 1 > Quantity 2

  2. Quantity 1 ≥ Quantity 2

  3. Quantity 2 > Quantity 1

  4. Quantity 2 ≥ Quantity 1

  5. Quantity 1 = Quantity 2 or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given the efficiency ratio 8:4:6:3, let the rates be 8k, 4k, 6k, 3k. Quantity 1 (A+B) rate = 12k. Quantity 2 (C+D) rate = 9k. Since the total work is constant, the time taken is inversely proportional to the rate. A higher rate means less time, so Quantity 2 takes more time than Quantity 1.

AI explanation

Let the efficiencies of A, B, C and D be 8, 4, 6 and 3 units respectively, making their combined efficiency 21 units per day. The total work is 21 units per day multiplied by 40/7 days, which equals 120 units. For Quantity 1, the time taken by A and B together is 120 / (8 + 4) = 10 days. For Quantity 2, the time taken by C and D together is 120 / (6 + 3) = 13.33 days. Therefore, Quantity 2 is greater than Quantity 1.

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