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.
A. 2/3 Itrs B. 3 Itrs C. 5 litre D. 7 Itrs
Correct Answer: 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.