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. 14 L
B. 21 L
C. 28 L
D. 70 L

Answer

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

1. **Define the Total Capacity**: Let the total capacity of the beaker be represented as \( a \) liters.

2. **Determine the Amount of Water Currently in the Beaker**: The beaker is currently \( \frac{3}{7} \) filled with water. Therefore, the amount of water in the beaker is:
\[ \text{Water in beaker} = \frac{3}{7}a \]

3. **Identify the Additional Water Needed**: We know that an additional 16 liters of water is needed to fill the beaker to its brim. This means that the total amount of water when the beaker is full is:
\[ \text{Total water when full} = \text{Water in beaker} + \text{Additional water needed} \]
This can be expressed as:
\[ a = \frac{3}{7}a + 16 \]

4. **Rearranging the Equation**: To find \( a \), we rearrange the equation:
\[ a - \frac{3}{7}a = 16 \]
This simplifies to:
\[ \frac{4}{7}a = 16 \]

5. **Solving for \( a \)**: To isolate \( a \), multiply both sides by the reciprocal of \( \frac{4}{7} \):
\[ a = 16 \times \frac{7}{4} \]
Simplifying this gives:
\[ a = 16 \times 1.75 = 28 \]

6. **Conclusion**: The capacity of the beaker is:
\[ \text{Capacity of the beaker} = 28 \text{ liters} \]