Multiple choice

Find the value of both quantities and state the correct relationship.\newline Quantity I: Days in which B can complete work alone, if A and B can complete work in 40 days, B and C in 20 days and C and A in 30 days.\newline Quantity II: Days in which B can complete work alone, if A and B can complete work in 24 days and A is 50% more efficient than B.

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

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

Quantity I: From (A+B) = 1/40, (B+C) = 1/20, (C+A) = 1/30. Adding all: 2(A+B+C) = 1/40 + 1/20 + 1/30 = 13/120. So A+B+C = 13/240. B's rate = (A+B+C) - (A+C) = 13/240 - 1/30 = 3/240 = 1/80. B alone takes 80 days. Quantity II: A+B = 1/24 and A is 50% more efficient than B, so A = 1.5B. Then 2.5B = 1/24, B = 1/60. B alone takes 60 days. Since 60 < 80, Quantity II (smaller days) represents faster completion, so B's capacity is higher.

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