A container was `1/4` filled with water .When `1.4` L of water was poured into the container , it becomes `1/3` filled .What is the capacity of the container ?

Options

A. `8.2` L
B. `12.6` L
C. `4.8` L
D. `16.8` L

Answer

To solve the problem step by step, let's denote the capacity of the container as \( x \) liters.

### Step 1: Establish the initial condition
The container is initially \( \frac{1}{4} \) filled with water. Therefore, the amount of water in the container initially is:
\[ \text{Initial water} = \frac{1}{4}x \]

### Step 2: Add the additional water
When \( 1.4 \) liters of water is added to the container, the new amount of water in the container becomes:
\[ \text{New water amount} = \frac{1}{4}x + 1.4 \]

### Step 3: Set up the equation for the new condition
After adding \( 1.4 \) liters of water, the container is now \( \frac{1}{3} \) filled. Therefore, we can write the equation:
\[ \frac{1}{4}x + 1.4 = \frac{1}{3}x \]

### Step 4: Solve the equation
To solve for \( x \), we first eliminate the fractions by finding a common denominator. The least common multiple of \( 4 \) and \( 3 \) is \( 12 \). We multiply the entire equation by \( 12 \):
\[ 12 \left( \frac{1}{4}x \right) + 12(1.4) = 12 \left( \frac{1}{3}x \right) \]
This simplifies to:
\[ 3x + 16.8 = 4x \]

### Step 5: Rearrange the equation
Now, we can rearrange the equation to isolate \( x \):
\[ 16.8 = 4x - 3x \]
\[ 16.8 = x \]

### Step 6: Conclusion
Thus, the capacity of the container is:
\[ \boxed{16.8 \text{ liters}} \]