Three bottles of equal capacity have mixture of milk and water in ratio 5 : 7, 7 : 9 and 2 : 1 respectively. These three bottles are emptied into a large bottle. What is the percentage of milk in the new mixture?

Step 1: Understand the setup

• Three bottles have the same capacity. Let each be 1 litre for simplicity.
• Mixtures in the bottles are in the ratios:
  • Bottle 1: Milk : Water = 5 : 7 ⇒ Total parts = 12
  • Bottle 2: Milk : Water = 7 : 9 ⇒ Total parts = 16
  • Bottle 3: Milk : Water = 2 : 1 ⇒ Total parts = 3

Step 2: Calculate milk in each bottle

Bottle 1: Milk = (5 / 12) × 1 = 0.4167 litres
Bottle 2: Milk = (7 / 16) × 1 = 0.4375 litres
Bottle 3: Milk = (2 / 3) × 1 = 0.6667 litres

Total milk = 0.4167 + 0.4375 + 0.6667 = 1.5209 litres

Total mixture = 3 litres (since 1 litre from each bottle)

Step 3: Calculate percentage of milk in the mixture

Percentage of milk = (Total milk / Total mixture) × 100
                   = (1.5209 / 3) × 100
                   ≈ 50.7%

Answer: Approximately 50.7% of the mixture is milk.

By averaging the ratios by volume, weighted equally, we calculate the final milk concentration in the combined mixture.