Question

in a mixture of 45 litres, the ratio of water to milk is 2:13,. find how much water must be added to this
mixture to make the ratio of milk to water 3:1

Answer 1

We know that total volume of mixture is 45 liters. And ratio of water to milk is $\frac{\text{water}}{\text{milk}} = \frac{2}{13}$. In this case we can find how much milk in this mixture:

$\text{milk} = 45 \cdot \frac{13}{15} = 39$. So, there is 39 liters of milk in this mixture. And in this mixture we have already $\text{water} = 45 - 39 = 6:6$ liters of water.

If we need for ratio $\frac{\text{milk}}{\text{water}} = \frac{3}{1}$, then we will have that: $\frac{\text{milk}}{\text{water}} = \frac{39}{x} = \frac{3}{1} \Rightarrow x = 13$. It means that we need to have 13 liters of water to have ratio $\frac{\text{milk}}{\text{water}} = \frac{3}{1}$.

As we have already 5 liters of water then we need to add $\Delta \text{water} = 13 - 6 = 7:7$ liters of water to have ratio $\frac{\text{milk}}{\text{water}} = \frac{3}{1}$.

**Answer:** 7 liters.