Multiple choice

In the following questions, two equations Quantity I and Quantity II are given. You have to solve both the equations and give answer. Quantity I: If A and B can complete work in 40 days, B and C in 20 days and C and A in 30 days, then find out in how many days B alone can complete the work? Quantity II: If A and B can complete work in 24 days and A is 50% more efficient than B. then find in how many days B alone can 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 the relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity I: A + B = 1/40 (work per day). B + C = 1/20. C + A = 1/30. Adding all: 2(A + B + C) = 1/40 + 1/20 + 1/30 = 3/120 + 6/120 + 4/120 = 13/120. So A + B + C = 13/240. B = (A + B + C) - (A + C) = 13/240 - 1/30 = 13/240 - 8/240 = 5/240 = 1/48. B alone takes 48 days. Quantity II: B's efficiency = x. A's efficiency = 1.5x (50% more). A + B = 2.5x = 1/24. x = 1/60. B alone takes 60 days. Since 48 < 60, Quantity I < Quantity II.

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