A mixture contains alcohol and water in the ratio 4:3. If 5 litres of water is added to the mixture, the ratio becomes 4: 5. The quantity of alcohol in the given mixture is

Options

A. 3litres
B. 4litres
C. 10litres
D. 5litres

Answer

To find the quantity of alcohol in the given mixture, we can follow these steps:

### Step 1: Understand the initial ratio
The initial ratio of alcohol to water is given as 4:3. This means for every 4 parts of alcohol, there are 3 parts of water.

### Step 2: Set up the variables
Let the quantity of alcohol be \(4x\) liters and the quantity of water be \(3x\) liters, where \(x\) is a common multiplier.

### Step 3: Add the water
According to the problem, 5 liters of water is added to the mixture. Therefore, the new quantity of water becomes:
\[ 3x + 5 \text{ liters} \]

### Step 4: Set up the new ratio
After adding the water, the new ratio of alcohol to water is 4:5. We can express this as:
\[ \frac{4x}{3x + 5} = \frac{4}{5} \]

### Step 5: Cross-multiply to solve for \(x\)
Cross-multiplying gives us:
\[ 4 \cdot (3x + 5) = 5 \cdot 4x \]
Expanding both sides:
\[ 12x + 20 = 20x \]

### Step 6: Rearranging the equation
Rearranging the equation to isolate \(x\):
\[ 20x - 12x = 20 \]
\[ 8x = 20 \]
\[ x = \frac{20}{8} = 2.5 \]

### Step 7: Calculate the quantity of alcohol
Now, substituting \(x\) back to find the quantity of alcohol:
\[ \text{Quantity of alcohol} = 4x = 4 \cdot 2.5 = 10 \text{ liters} \]

### Final Answer
The quantity of alcohol in the given mixture is **10 liters**.

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