A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Question
A milk vendor has 2 cans of milk. The first contains 25% water and the rest milk. The second contains 50% water. How much milk should he mix from each of the containers so as to get 12 litres of milk such that the ratio of water to milk is 3 : 5?
Solution
Let's denote:
- The amount of milk from the first can as x litres.
- The amount of milk from the second can as (12 - x) litres, because the total amount of milk is 12 litres.
The first can contains 25% water and 75% milk, so the amount of milk in the first can is 0.75x litres.
The second can contains 50% water and 50% milk, so the amount of milk in the second can is 0.5(12 - x) litres.
The total amount of milk is the sum of the milk from the first can and the second can, which is 0.75x + 0.5(12 - x).
The total amount of water is the sum of the water from the first can and the second can, which is 0.25x + 0.5(12 - x).
According to the problem, the ratio of water to milk is 3 : 5, so we can set up the equation:
(0.25x + 0.5(12 - x)) / (0.75x + 0.5(12 - x)) = 3 / 5
Solving this equation will give us the value of x, which is the amount of milk that should be mixed from the first can. The amount of milk that should be mixed from the second can is 12 - x.
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