Multiple choice

A container, whose capacity is 81 l, contains milk and water in the ratio of 5 : 4. What quantity of the mixture should be replaced with pure milk so that in the final mixture, the ratio of milk to water becomes 6 : 4?

  1. 8 l

  2. 8.1 l

  3. 8.5 l

  4. 9 l

  5. 9.3 l
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Total = 81L. Milk = 45L, Water = 36L. Replacing x liters of mixture: Milk removed = (5/9)x, Water removed = (4/9)x. New Milk = 45 - (5/9)x + x = 45 + (4/9)x. New Water = 36 - (4/9)x. Ratio (45 + 4/9x) / (36 - 4/9x) = 6/4 = 1.5. 45 + 4/9x = 54 - 6/9x => 10/9x = 9 => x = 8.1.

AI explanation

The initial mixture contains 45 litres of milk and 36 litres of water. When x litres of the mixture are replaced with pure milk, the amount of water remaining becomes 36 - (x times 36/81), which is 36 - 4x/9. Since the final ratio of milk to water must be 6:4, or 3:2, the final amount of water can be found by keeping the water constant and setting the total mixture to 27/2 parts of water, yielding a final water volume of 32.4 litres. Setting up the equation 36 - 4x/9 = 32.4, we find that 4x/9 equals 3.6, solving to x = 8.1 litres.

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