A small tank is 2/5 full of water. The water is then poured into a large empty tank which has a capacity which is twice that of the small tank. What fraction of the large tank is filled with water?

Options

A. `3/5`
B. `2/5`
C. `1/5`
D. `4/5`

Answer

To solve the problem step by step, we will follow these instructions:

1. **Identify the capacity of the small tank**: Let's denote the capacity of the small tank as \( x \).

2. **Determine the capacity of the large tank**: Since the large tank has a capacity that is twice that of the small tank, we can express the capacity of the large tank as \( 2x \).

3. **Calculate the amount of water in the small tank**: The small tank is \( \frac{2}{5} \) full of water. Therefore, the amount of water in the small tank can be calculated as:
\[ \text{Amount of water} = \frac{2}{5} \times x \]

4. **Pour the water into the large tank**: The amount of water from the small tank is poured into the large tank. We need to find out what fraction of the large tank this amount of water fills.

5. **Calculate the fraction of the large tank filled with water**: To find the fraction of the large tank that is filled with water, we divide the amount of water by the capacity of the large tank:
\[ \text{Fraction filled} = \frac{\text{Amount of water}}{\text{Capacity of large tank}} = \frac{\frac{2}{5} \times x}{2x} \]

6. **Simplify the expression**:
\[ \text{Fraction filled} = \frac{\frac{2}{5} \times x}{2x} = \frac{2}{5} \times \frac{1}{2} = \frac{2}{10} = \frac{1}{5} \]

Thus, the fraction of the large tank that is filled with water is \( \frac{1}{5} \).