Multiple choice

Directions: In the following item, Quantity I and Quantity II are given. Determine the relationship between the quantities and choose the appropriate option. Three workers, A, B, and C, can complete a task in 12, 15, and 20 days, respectively, working alone. Quantity I: The total number of days it would take for workers A and B to complete the task if they work together Quantity II: The number of days it would take for workers B and C to complete the entire task if they work together

  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 No relation
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Quantity I: A and B together = 1 / (1/12 + 1/15) = 1 / (9/60) = 60/9 = 6.67 days. Quantity II: B and C together = 1 / (1/15 + 1/20) = 1 / (7/60) = 60/7 = 8.57 days. Since 6.67 < 8.57, Quantity I < Quantity II.

AI explanation

Using the LCM method, assume the total work is the least common multiple of 12, 15, and 20, which is 60 units. The efficiencies of A, B, and C are 5, 4, and 3 units per day respectively. Quantity I is the time taken by A and B together, calculated as 60 divided by their combined efficiency of 9, giving 6.67 days. Quantity II is the time taken by B and C together, calculated as 60 divided by their combined efficiency of 7, giving 8.57 days, showing that Quantity I is less than Quantity II.

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