Question

The ratio of milk and water in a mixture is 3:5. We added 10 liters of water to the mixture, then the ratio becomes 3:7. Find the initial quantity of milk.

Answer 1

To find the initial quantity of milk, we set up a proportion based on the given ratios and added water volume. After solving, we determined the initial quantity of milk to be 15 liters.

Step-by-step explanation:

The student asked for help in finding the initial quantity of milk in a mixture where the ratio of milk to water was initially 3:5 and after adding 10 liters of water became 3:7.

Step-by-Step Solution

Let's assume the initial quantity of milk to be 3x liters and the initial quantity of water to be 5x liters. The question states that by adding 10 liters of water to the mixture, the new ratio becomes 3:7. This can be expressed as:

3x / (5x + 10) = 3/7

Cross-multiply to solve for x:

3x * 7 = 3 * (5x + 10)

21x = 15x + 30

Simplify and solve for x:

21x - 15x = 30

6x = 30

x = 30 / 6

x = 5

The initial quantity of milk, represented as 3x, would therefore be:

3 * 5 = 15 liters