Mixture Ratio Problem: Calculating Added Water
This problem involves calculating the amount of water to add to a milk and water mixture to achieve a specific ratio. We need to find the initial quantities and then determine how much water to add.
Initial Mixture Quantities
The total volume of the mixture is 85 Liters.
The initial ratio of milk to water is 27 : 7.
- Total ratio parts = $27 + 7 = 34$ parts.
- Amount of Milk = $\frac{27}{34} \times 85$ L
- Amount of Water = $\frac{7}{34} \times 85$ L
Calculating the amounts:
- Milk = $\frac{27 \times 85}{34} = \frac{27 \times 5}{2} = \frac{135}{2} = 67.5$ L
- Water = $\frac{7 \times 85}{34} = \frac{7 \times 5}{2} = \frac{35}{2} = 17.5$ L
Check: $67.5 + 17.5 = 85$ L. The initial quantities are correct.
Calculating Added Water
We want the new ratio of milk to water to be 3 : 1. Only water is added, so the amount of milk remains constant (67.5 L).
Let the amount of water added be $x$ Liters.
The new amount of water will be $(17.5 + x)$ L.
Set up the equation based on the desired final ratio:
$ \frac{\text{Amount of Milk}}{\text{New Amount of Water}} = \frac{3}{1} $
$ \frac{67.5}{17.5 + x} = \frac{3}{1} $
Now, solve for $x$:
- Cross-multiply: $67.5 = 3 \times (17.5 + x)$
- Distribute: $67.5 = 52.5 + 3x$
- Isolate the term with $x$: $3x = 67.5 - 52.5$
- Calculate the difference: $3x = 15$
- Solve for $x$: $x = \frac{15}{3}$
- Result: $x = 5$ L
Therefore, 5L of water should be added.
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Important Questions from Mixture and Alligation
My father is presently 25 years older than me. The sum of our ages 5 years ago was 39 years. Find my present age.
Rice worth ₹43/kg and ₹67/kg are mixed with a third variety in the ratio 2 : 1 : 5. If the mixture is worth ₹96/kg, the price (in ₹) of the third variety of rice per kg will be:
42 litres of milk at ₹25 per litre is mixed with 28 litres of milk at ₹40 per litre. Find the average price of the mixture.
15 kg of ₹10 per kg wheat is mixed with 5 kg of another type of wheat to get a mixture costing ₹30 per kg. Find the price (per kg) of the costlier wheat.
If a + b + c = 0, then the value of (a² + b² + 2ab) is equal to:
