Multiple choice

Passage

Directions: In the following item, quantity I and quantity II are given. Determine the relationship between the quantities and choose the appropriate option. (1) If Quantity I ≥ Quantity II (2) If Quantity I > Quantity II (3) If Quantity I < Quantity II (4) If Quantity I = Quantity II or the relationship cannot be established from the information given (5) If Quantity I ≤ Quantity II

A drum has 120 litres of a mixture containing milk and water in the ratio 5 : 1. Quantity I: The proportion of milk in the mixture after adding 30 litres of water. Quantity II: The proportion of milk in the mixture after 30 litres of mixture is replaced with water.

  1. (1)

  2. (2)

  3. (3)

  4. (4)

  5. (5)
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Initial: 100 milk, 20 water. Q1: Add 30 water -> 100 milk, 50 water. Proportion = 100/150 = 2/3. Q2: Replace 30 mixture (5:1 ratio, 25 milk, 5 water) with 30 water. Milk left = 100 - 25 = 75. Total = 120. Proportion = 75/120 = 5/8. 2/3 (0.66) > 5/8 (0.625).

AI explanation

The initial mixture contains 100 litres of milk and 20 litres of water. For Quantity I, adding 30 litres of water makes the total volume 150 litres, so the proportion of milk is 100 divided by 150, or 2/3. For Quantity II, replacing 30 litres of the mixture with water removes 25 litres of milk and 5 litres of water, leaving 75 litres of milk in a 120 litre mixture, making the proportion 75/120, which simplifies to 5/8. Comparing 2/3 (equal to 16/24) and 5/8 (equal to 15/24) shows that Quantity I is greater than Quantity II.

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