Mixture Ratio Calculation: Adding Water
This problem involves calculating the amount of water to add to a milk-water mixture to achieve a specific new ratio.
Initial Quantities Calculation
The initial mixture has a total volume of 120 litres with a milk to water ratio of $2:1$.
- Total parts in the ratio = $2 + 1 = 3$.
- Volume per part = $\frac{120 \text{ litres}}{3} = 40$ litres.
- Initial amount of Milk = $2 \times 40 = 80$ litres.
- Initial amount of Water = $1 \times 40 = 40$ litres.
Target Ratio Adjustment
The goal is to change the ratio to $1:2$ (Milk:Water) by adding only water. The amount of milk remains constant at 80 litres.
Let the amount of water added be $x$ litres.
The new amount of water will be $(40 + x)$ litres.
Solving for Added Water
The new ratio equation is:
$ \frac{\text{Milk}}{\text{New Water}} = \frac{80}{40 + x} $We need this ratio to be $1:2$. So:
$ \frac{80}{40 + x} = \frac{1}{2} $Cross-multiply to solve for $x$:
$ 80 \times 2 = 1 \times (40 + x) $ $ 160 = 40 + x $ $ x = 160 - 40 $ $ x = 120 \text{ litres} $Conclusion
To achieve the desired milk to water ratio of $1:2$, 120 litres of water must be added to the mixture.
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