Multiple choice

A can contains a mixture of two liquids, milk and water, in the ratio 7:5. When 9 litres of the mixture are drawn off and the can is filled with water, the ratio of milk and water becomes 7:9. How many litres of milk were contained in the can initially?

  1. 26

  2. 17

  3. 21

  4. 27

  5. 29
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the initial amounts be 7x and 5x. When 9 litres are removed, 5.25 litres of milk and 3.75 litres of water are removed. After adding 9 litres of water, the new ratio is (7x - 5.25) / (5x - 3.75 + 9) = 7/9. Solving for x yields x = 3. Initial milk = 7*3 = 21 litres.

AI explanation

Let the initial total volume of the mixture be V, so the initial milk is 7V/12 and water is 5V/12. When 9 liters are removed and replaced with water, the remaining milk is 7(V minus 9)/12. Setting this equal to the new quantity of milk, which is 7/16 of the total volume V, gives 7(V minus 9)/12 = 7V/16. Solving this equation yields V = 36, meaning the initial amount of milk was 7/12 of 36, which is 21 liters.

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