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A mixture contains milk and water in a ratio 12 : 5. On adding 12 liters of water, the ratio of milk to water becomes 9 : 4. The quantity of milk in the mixture is:

Question

A mixture contains milk and water in a ratio 12 : 5. On adding 12 liters of water, the ratio of milk to water becomes 9 : 4. The quantity of milk in the mixture is:

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Solution

Step 1: Let's denote the initial quantity of milk as 12x and the initial quantity of water as 5x (since the ratio is 12:5).

Step 2: According to the problem, when 12 liters of water is added, the ratio of milk to water becomes 9:4. So, we can write this as 12x/(5x + 12) = 9/4.

Step 3: Cross-multiply to solve for x. This gives us 48x = 45x + 108.

Step 4: Subtract 45x from both sides to isolate x. This gives us 3x = 108.

Step 5: Divide both sides by 3 to solve for x. This gives us x = 36.

Step 6: The quantity of milk in the mixture is 12x, so substitute x = 36 into this equation to find the quantity of milk. This gives us 12*36 = 432 liters.

So, the quantity of milk in the mixture is 432 liters.

This problem has been solved

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