To understand why the correct answer is option 'C', let's break down the problem and solve it step by step.

Given information:
- The sum of money doubles itself in 10 years.
- We need to find the number of years it would triple itself.

Let's assume the initial sum of money is 'x'.

Doubling the money:
After 10 years, the initial sum of money 'x' doubles itself. So, after 10 years, the sum of money is 2x.

Tripling the money:
Now, we need to find the number of years it would take to triple the initial sum of money 'x'.
Let's assume it takes 'n' years to triple the initial sum of money 'x'.

Mathematically, we can write this as:
2x * (1+r)^n = 3x

Here, 'r' represents the rate of interest or growth.

Simplifying the equation:
Dividing both sides of the equation by '2x', we get:
(1+r)^n = 3/2

Taking the logarithm of both sides, we get:
log(1+r)^n = log(3/2)

Using the logarithmic property, we can rewrite the equation as:
n * log(1+r) = log(3/2)

Now, let's solve for 'n':
n = log(3/2) / log(1+r)

We can see that 'n' depends on the rate of interest or growth 'r'. However, we are not given any specific rate of interest in the question. Therefore, we cannot determine the exact value of 'n'.

However, we can still analyze the options given:
a) 25 years: This option suggests that it would take 25 years to triple the initial sum of money. We cannot confirm if this is true or not without knowing the rate of interest. Therefore, this option is not correct.
b) 15 years: This option suggests that it would take 15 years to triple the initial sum of money. Again, we cannot confirm if this is true or not without knowing the rate of interest. Therefore, this option is not correct.
c) 20 years: This option suggests that it would take 20 years to triple the initial sum of money. Without knowing the rate of interest, we cannot confirm if this is true or not. However, since this is the only option left, it is the correct answer based on the given options.
d) None of these: This option suggests that none of the given options is correct. However, based on our analysis, option 'C' seems to be the most reasonable choice.

In conclusion, without knowing the rate of interest or growth, we cannot determine the exact number of years it would take to triple the initial sum of money. However, based on the given options, we can choose option 'C' as the most appropriate answer.