Multiple choice

How many litres of a mixture in an 80-litre bottle, full of 80% concentrated milk, will have to be replaced with water to make the resultant mixture 60% concentrated?

  1. 10 litres

  2. 15 litres

  3. 20 litres

  4. 30 litres
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let x be the amount replaced. The amount of milk initially is 0.8 * 80 = 64 litres. After replacing x litres with water, the remaining milk is 64 - 0.8x. We want this to be 60% of 80, which is 48 litres. So, 64 - 0.8x = 48, which gives 0.8x = 16, so x = 20.

AI explanation

Using the mixture replacement formula, the final concentration equals the initial concentration multiplied by (1 minus y divided by x), where x is the total capacity and y is the replaced amount. Substituting the given values results in 60 = 80 times (1 minus y divided by 80). Solving this equation, 0.75 equals 1 minus y divided by 80, yielding y equals 20 litres.

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