Multiple choice

Find the value of both quantities and then state the correct relationship. (10) litres of water were drawn from a cask full of water and it was filled with (30) litres milk then the concentration of milk in the mixture become (20\%). ()(\textbf{Quantity I :} ) From initial water, how many litres of mixture should be replaced with (10) litres milk so the concentration of water in the mixture will become (60\%). ()(\textbf{Quantity II :} ) What was the original quantity of water in the cask?

  1. Quantity I > Quantity II

  2. Quantity I ≥ Quantity II

  3. Quantity II > Quantity I

  4. Quantity II ≥ Quantity I

  5. Quantity I = Quantity II or Relation cannot be established
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let original water = W liters. After removing 10L water and adding 30L milk, total = W + 20L. Milk concentration = 20%, so 30/(W+20) = 0.2, giving W = 130L. For Quantity I: let M be mixture to replace. After removing M and adding 10L milk, water = (130-M)/140 × 100 = 60%. Solving gives M = 46L. Quantity I = 46, Quantity II = 130. Since 46 < 130, Quantity II > Quantity I.

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