A mixture contains acid and water in the ratio of 7 : 3. If 4 litres of water is added to it, then the ratio of acid and water becomes 7 : 4. What is the quantity (in litres) of acid in the mixture?

Options

A. 28
B. 22
C. 20
D. 32

Answer

To solve the problem step by step, let's denote the quantities of acid and water in the mixture.

### Step 1: Define the initial quantities
Let the quantity of acid be \( 7x \) liters and the quantity of water be \( 3x \) liters, where \( x \) is a common multiplier.

### Step 2: Add the additional water
According to the problem, 4 liters of water is added to the mixture. Therefore, the new quantity of water becomes:
\[ 3x + 4 \text{ liters} \]

### Step 3: Set up the new ratio
After adding the water, the new ratio of acid to water is given as 7:4. We can set up the equation based on this ratio:
\[ \frac{7x}{3x + 4} = \frac{7}{4} \]

### Step 4: Cross-multiply to solve for \( x \)
Cross-multiplying gives us:
\[ 7x \cdot 4 = 7 \cdot (3x + 4) \]
This simplifies to:
\[ 28x = 21x + 28 \]

### Step 5: Isolate \( x \)
Now, we can isolate \( x \) by subtracting \( 21x \) from both sides:
\[ 28x - 21x = 28 \]
\[ 7x = 28 \]

### Step 6: Solve for \( x \)
Dividing both sides by 7 gives:
\[ x = 4 \]

### Step 7: Calculate the quantity of acid
Now that we have \( x \), we can find the quantity of acid:
\[ \text{Quantity of acid} = 7x = 7 \cdot 4 = 28 \text{ liters} \]

### Final Answer
The quantity of acid in the mixture is \( 28 \) liters.

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