Multiple choice

A mixture contains milk and water in the ratio 5 : 3. If 16 litres of mixture is replaced by 16 litres of water, then the ratio becomes 3 : 5. How many litres of milk was there in the mixture initially.

  1. 8 litre

  2. 16 litre

  3. 24 litre

  4. 25 litre

  5. 40 litre
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Initial milk:water = 5:3, so milk = 5x, water = 3x, total = 8x. 16 litres removed contains milk = 5x/8x × 16 = 10 litres, water = 3x/8x × 16 = 6 litres. After removal: milk = 5x-10, water = 3x-6. Adding 16 litres water: milk = 5x-10, water = 3x-6+16 = 3x+10. New ratio (5x-10):(3x+10) = 3:5. Cross-multiplying: 5(5x-10) = 3(3x+10), 25x-50 = 9x+30, 16x = 80, x = 5. Initial milk = 5x = 5×5 = 25 litres. Options A, B, C, and E are incorrect.

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