Acid Water Ratio Problem Solution
This solution addresses a mixture problem involving the ratio of acid and water in a 50-liter solution. The goal is to determine how much water needs to be added to change the initial ratio of 3:2 (acid:water) to 1:1.
Calculate Initial Acid and Water Volumes
The total volume is 50 liters, with acid and water in a 3:2 ratio.
- The sum of the ratio parts is $3 + 2 = 5$.
- Each part represents $\frac{50 \text{ L}}{5} = 10 \text{ L}$.
- Initial acid volume is $3 \times 10 \text{ L} = 30 \text{ L}$.
- Initial water volume is $2 \times 10 \text{ L} = 20 \text{ L}$.
Determine Amount of Water to Add
Let the amount of water added be '$x$' liters.
The acid volume remains 30 L.
The new water volume becomes $(20 + x)$ L.
We want the new ratio of acid to water to be 1:1.
Set up the equation based on the desired ratio:
$ \frac{\text{Acid Volume}}{\text{New Water Volume}} = \frac{1}{1} $ $ \frac{30}{20 + x} = \frac{1}{1} $Solve for '$x$':
Cross-multiply:
$ 30 \times 1 = 1 \times (20 + x) $ $ 30 = 20 + x $Isolate '$x$':
$ x = 30 - 20 $ $ x = 10 \text{ L} $Confirm Final Ratio
Adding 10 L of water results in:
- New water volume = $20 \text{ L} + 10 \text{ L} = 30 \text{ L}$.
- Acid volume = $30 \text{ L}$.
- The new ratio is $30 \text{ L} : 30 \text{ L}$, which simplifies to $1:1$.
The amount of water to be added is 10 L.
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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:
