Multiple choice

In the following questions, Quantity I and Quantity II are given. You have to solve both them and give answer. Quantity I: The ratio of amrit to amrita age is 7: 5 and the sum of their ages is 72. Then find the total ages after 12 years? Quantity II: The average age of the whole class is 12.05 years. The average age of the girls is 12.5 years and the average age of 45 boys is 11.75 years. Then find the total number girls in the class?

  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

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A Correct answer
Explanation

Quantity I: Ratio 7:5, sum 72. So 7x + 5x = 72, 12x = 72, x = 6. Amrit = 42, Amrita = 30. After 12 years: 42+12 = 54, 30+12 = 42. Total = 54+42 = 96. Quantity II: Class average 12.05 with 45 boys avg 11.75 and girls avg 12.5. Let g = number of girls. Total average = (45×11.75 + g×12.5)/(45+g) = 12.05. Solving: 528.75 + 12.5g = 542.25 + 12.05g. 0.45g = 13.5, g = 30. So 30 girls. Comparing: Quantity I = 96, Quantity II = 30. Therefore Quantity I > Quantity II.