Given information:
- We have two volumes of solutions, one with pH = 4 and one with pH = 10.
- We are asked to determine the pH of the resulting solution when these volumes are mixed.

To solve this problem, let's analyze the concept of pH and its relationship with acidity and basicity.

Understanding pH:
- pH is a measure of the acidity or basicity of a solution.
- It is a logarithmic scale ranging from 0 to 14.
- A pH value of 7 is considered neutral, below 7 is acidic, and above 7 is basic.

pH of individual solutions:
- The solution with pH = 4 is acidic.
- The solution with pH = 10 is basic.

Mixing acidic and basic solutions:
- When an acidic solution is mixed with a basic solution, a neutralization reaction occurs.
- The resulting solution will have a pH closer to 7, which is neutral.

Explanation:
- In this case, mixing a solution with pH = 4 and a solution with pH = 10 will result in a neutralization reaction.
- The acidic solution will donate hydrogen ions (H+) to the basic solution, which will accept these hydrogen ions.
- The reaction will lead to the formation of water, which is neutral.
- As a result, the pH of the resulting solution will be closer to 7, indicating neutrality.

Answer:
- Therefore, the correct answer is option 'c' - 7.

Note:
- It is important to remember that the pH of the resulting solution is not the average of the pH values of the individual solutions.