A mixture contains alcohol and water in the ratio 2:1. If 3 litres of water is added to the mixture, the ratio becomes 2:3. Find the 2 quantity of alcohol in the given mixture.
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Correct Answer: Option B
Explanation:
Let's solve the problem step by step:
1. Initial Mixture Ratio:
The initial ratio of alcohol to water is \(2:1\). Let the amount of alcohol be \(2x\) liters and the amount of water be \(x\) liters.
2. Mixture after Adding Water:
When 3 liters of water is added, the new amount of water becomes \(x + 3\) liters.
3. New Ratio:
After adding the water, the ratio of alcohol to water becomes \(2:3\). Therefore:
\[
\frac{2x}{x + 3} = \frac{2}{3}
\]
4. Solve for \(x\):
- Cross-multiply to solve the proportion:
\[
2x \cdot 3 = 2 \cdot (x + 3)
\]
\[
6x = 2x + 6
\]
- Subtract \(2x\) from both sides:
\[
4x = 6
\]
- Divide by 4:
\[
x = \frac{6}{4} = 1.5
\]
5. Calculate the Amount of Alcohol:
- The amount of alcohol is \(2x\):
\[
2 \cdot 1.5 = 3 \text{ liters}
\]
The quantity of alcohol in the given mixture is 3 liters.
The correct answer is B. 3 liters.
Let's solve the problem step by step:
1. Initial Mixture Ratio:
The initial ratio of alcohol to water is \(2:1\). Let the amount of alcohol be \(2x\) liters and the amount of water be \(x\) liters.
2. Mixture after Adding Water:
When 3 liters of water is added, the new amount of water becomes \(x + 3\) liters.
3. New Ratio:
After adding the water, the ratio of alcohol to water becomes \(2:3\). Therefore:
\[
\frac{2x}{x + 3} = \frac{2}{3}
\]
4. Solve for \(x\):
- Cross-multiply to solve the proportion:
\[
2x \cdot 3 = 2 \cdot (x + 3)
\]
\[
6x = 2x + 6
\]
- Subtract \(2x\) from both sides:
\[
4x = 6
\]
- Divide by 4:
\[
x = \frac{6}{4} = 1.5
\]
5. Calculate the Amount of Alcohol:
- The amount of alcohol is \(2x\):
\[
2 \cdot 1.5 = 3 \text{ liters}
\]
The quantity of alcohol in the given mixture is 3 liters.
The correct answer is B. 3 liters.