Multiple choice

A container contains 60 litres of milk. Some milk is replaced by water twice. Each time 12 litres of mixture is replaced. After the two replacements, what is the final ratio of milk to water?

  1. 16 : 9

  2. 18 : 7

  3. 17 : 3

  4. 11 : 4

  5. 15 : 4
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A Correct answer
Explanation

Using the formula for replacement, the final amount of milk is M = M_0 * (1 - x/V)^n. Here M_0 = 60, x = 12, V = 60, n = 2. M = 60 * (1 - 12/60)^2 = 60 * (0.8)^2 = 60 * 0.64 = 38.4. The amount of water is 60 - 38.4 = 21.6. The ratio of milk to water is 38.4 : 21.6 = 384 : 216 = 16 : 9.

AI explanation

Using the replacement formula, the final quantity of milk is calculated as Initial Amount * (1 - Replacement Amount / Total Amount)^n. Plugging in the values gives 60 * (1 - 12/60)^2 = 60 * (4/5)^2 = 60 * 16/25 = 38.4 litres. The water is 60 - 38.4 = 21.6 litres, making the ratio of milk to water 38.4 to 21.6, which simplifies to 16 to 9.

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