Multiple choice

Directions: Compare the two quantities in A and B. A, B and C can complete a work in 20, 24 and 30 days respectively. Quantity A Quantity B The time required to complete the work if A, B and C work together. The time required by B alone to complete one third of the work.

  1. Quantity A is greater than quantity B.

  2. Quantity B is greater than quantity A.

  3. Both quantities are equal.

  4. The relationship between the quantities cannot be determined.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Quantity A: 1/20 + 1/24 + 1/30 = (6+5+4)/120 = 15/120 = 1/8. Time = 8 days. Quantity B: B takes 24 days for the whole work, so 1/3 of the work takes 24/3 = 8 days. Both are 8 days.

AI explanation

Using the LCM method, let the total work be 120 units. The efficiencies of A, B and C are 6, 5 and 4 units per day respectively. Working together, their combined efficiency is 15 units per day, so Quantity A is 120 divided by 15, which is 8 days. For Quantity B, B alone takes 120 divided by 5 days for the full work, making it 24 days; therefore one third of the work takes 8 days. Both quantities are equal.

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