A beaker is `(3)/(7)`th filled with water. Another 16 L of water is needed to fill the beaker to its brim. What is the capacity of the beaker?

Options

A. 28 L
B. 14 L
C. 50 L
D. 100 L

Explanation

To find the capacity of the beaker, we can follow these steps:

### Step 1: Understand the problem
The beaker is currently filled to \( \frac{3}{7} \) of its total capacity. We need to find out how much water is required to fill it completely, which is given as 16 liters.

### Step 2: Calculate the remaining capacity
The fraction of the beaker that is not filled with water is:
\[ 1 - \frac{3}{7} = \frac{4}{7} \]
This means \( \frac{4}{7} \) of the beaker's total capacity is still empty.

### Step 3: Set up the equation
Let \( C \) be the total capacity of the beaker. According to the problem, the remaining capacity \( \frac{4}{7}C \) is equal to 16 liters:
\[ \frac{4}{7}C = 16 \]

### Step 4: Solve for \( C \)
To find \( C \), we can multiply both sides of the equation by \( \frac{7}{4} \):
\[ C = 16 \times \frac{7}{4} \]
Calculating the right side:
\[ C = 16 \times 1.75 = 28 \]

### Step 5: Conclusion
Thus, the total capacity of the beaker is:
\[ \boxed{28 \text{ liters}} \]

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