Let's assume the two numbers as x and y.

Given:
Sum of two numbers = 25
Product of two numbers = 156

1. Formulating the equations:
From the given information, we can form the following equations:

x + y = 25 ...(Equation 1)
xy = 156 ...(Equation 2)

2. Solving the equations:
To find the larger number, we need to determine the values of x and y. We can solve the equations simultaneously.

From Equation 1, we can express x in terms of y:
x = 25 - y

Substituting this value of x in Equation 2, we get:
(25 - y)y = 156

Expanding the equation:
25y - y^2 = 156

Rearranging the equation:
y^2 - 25y + 156 = 0

3. Factorizing the quadratic equation:
To solve the quadratic equation, we need to factorize it.
The factors of 156 that add up to -25 are -13 and -12.

Therefore, the quadratic equation can be factored as:
(y - 13)(y - 12) = 0

Setting each factor equal to zero, we get two possible values for y:
y - 13 = 0 => y = 13
y - 12 = 0 => y = 12

4. Determining the larger number:
Now that we have found the possible values of y, we can substitute them back into Equation 1 to find the corresponding values of x.

For y = 13:
x = 25 - y
x = 25 - 13
x = 12

For y = 12:
x = 25 - y
x = 25 - 12
x = 13

Comparing the values of x and y, we can see that the larger number is 13.

Therefore, the correct answer is option C) 13.