Multiple choice

Given below are two quantities named I and II. Based on the given data, you have to determine the relation between them and mark the answer Quantity I- A,B and C can do a piece of work in 24, 30 and 40 days respectively. How long will it take them to complete the work if only A and B work for the first 6 days and then C joins them? Quantity II- B can complete the work in 20 days. C is twice as efficient as B and A takes 2 days more than C to complete the work. Working together, in how many days they would complete the work?

  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 relation can not be established
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Quantity I: A's rate = 1/24, B's rate = 1/30. Combined rate = 3/40. In 6 days: 6 × 3/40 = 9/20 work done. Remaining = 11/20. All three together: 1/24 + 1/30 + 1/40 = 1/12. Time for remaining = (11/20)/(1/12) = 6.6 days. Total = 12.6 days. Quantity II: B takes 20 days, so rate = 1/20. C is twice efficient, so C takes 10 days (rate = 1/10). A takes 12 days (rate = 1/12). All three together: 1/20 + 1/10 + 1/12 = 31/120. Time = 120/31 = 3.87 days. Since 12.6 > 3.87, Quantity I > Quantity II.

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