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

Question

Accepted Answer

To determine the capacity of the beaker, we need to understand the relationship between the current volume of water in the beaker and the additional volume needed to fill it to the brim.

1. **Understanding the Problem:**
   - The beaker is currently 3/7th filled with water.
   - An additional 16 liters of water is required to fill the beaker completely.

2. **Setting Up the Equation:**
   - Let the total capacity of the beaker be $ C $ liters.
   - According to the problem, 3/7th of the beaker is already filled, which means the volume of water currently in the beaker is $ \frac{3}{7}C $.
   - The additional water needed to fill the beaker is 16 liters, which means the remaining volume is $ C - \frac{3}{7}C = 16 $.

3. **Solving the Equation:**
   - Simplify the equation: $ C - \frac{3}{7}C = 16 $.
   - This can be rewritten as $ \frac{4}{7}C = 16 $.
   - To find $ C $, multiply both sides by $ \frac{7}{4} $: 
     $$
     C = 16 \times \frac{7}{4} = 28
     $$

4. **Conclusion:**
   - The total capacity of the beaker is 28 liters, which corresponds to Option 4.

5. **Explanation of Incorrect Options:**
   - **Option 1 (14 L):** If the beaker's capacity were 14 liters, then 3/7th of it would be 6 liters, and the remaining volume would be 8 liters, not 16 liters. Therefore, this option is incorrect.
   - **Option 2 (50 L):** If the beaker's capacity were 50 liters, then 3/7th of it would be approximately 21.43 liters, and the remaining volume would be approximately 28.57 liters, not 16 liters. Therefore, this option is incorrect.
   - **Option 3 (100 L):** If the beaker's capacity were 100 liters, then 3/7th of it would be approximately 42.86 liters, and the remaining volume would be approximately 57.14 liters, not 16 liters. Therefore, this option is incorrect.

By following the logical steps and calculations, we confirm that the correct answer is indeed Option 4, with the beaker's capacity being 28 liters.