A cleansing agent is mixed with water in the ratio 1:7. In 400 L of solution, find the amount of the cleansing agent.

Answer

To solve the problem step by step, we will follow the given information about the ratio of the cleansing agent to water and the total volume of the solution.

### Step-by-Step Solution:

1. **Understand the Ratio**: The cleansing agent is mixed with water in the ratio of 1:7. This means for every 1 part of cleansing agent, there are 7 parts of water.

2. **Define Variables**: Let the amount of cleansing agent be \( x \) liters. According to the ratio, the amount of water will be \( 7x \) liters.

3. **Set Up the Equation**: The total volume of the solution is given as 400 liters. Therefore, we can write the equation:
\[ x + 7x = 400 \]

4. **Combine Like Terms**: Simplifying the left side of the equation gives:
\[ 8x = 400 \]

5. **Solve for \( x \)**: To find the value of \( x \), divide both sides of the equation by 8:
\[ x = \frac{400}{8} \]
\[ x = 50 \]

6. **Conclusion**: The amount of cleansing agent is \( 50 \) liters.

### Final Answer:
The amount of the cleansing agent in 400 liters of solution is **50 liters**.