Multiple choice

Directions: Question given below contains a statement followed by Quantity I and Quantity II. Find the relationship between them and choose the answer accordingly. A man can do a piece of work in 20 days. The efficiency of a woman is 100% more than that of the man. On each day, one man and two women together make 120 chairs. They do the same work everyday. Quantity I: If three men and one woman did the work each day, then in how many days would the work be finished? Quantity II: If five women work on each day, then in how many days would the work be finished?

  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 relationship cannot be established
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A Correct answer
Explanation

Man efficiency = 1 unit/day. Woman efficiency = 100% more = 2 units/day. 1 man + 2 women = 1 + 2(2) = 5 units/day. Total work = 120 chairs/day * 20 days = 2400 chairs. Quantity I: 3 men + 1 woman = 3(1) + 2 = 5 units/day. Days = 2400 / 5 = 480 days. Quantity II: 5 women = 5(2) = 10 units/day. Days = 2400 / 10 = 240 days. Quantity I > Quantity II.

AI explanation

Let the man's efficiency be 1 unit per day, making the woman's efficiency 2 units per day since she is 100% more efficient. The daily output of 1 man and 2 women is 5 units, which equals 120 chairs; thus, 1 unit equals 24 chairs. The total work for the project is 20 days * 1 unit/day = 20 units. For Quantity I, the daily work of 3 men and 1 woman is 5 units, so they complete the work in 20 / 5 = 4 days. For Quantity II, the daily work of 5 women is 10 units, so they complete the work in 20 / 10 = 2 days. Comparing the two quantities, 4 days is greater than 2 days. Quantity I > Quantity II.

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