Hi Pramit Chakraborty,

It is given that average of three numbers is 13.

Sum = 3*13 = 39

It is given, $$\ \frac{\ 39+n}{4}$$ is a odd number.
If we divide 39 by 4, we get 9.75

It is also given that $$\ \frac{\ 39+n}{4}$$ is a odd number, after 9, 11 is the odd number.
39+n should be a number such that when it is divided by 4, it gives a odd number greater than 9, here the number will be 11.

Minimum value $$\ \frac{\ 39+n}{4}$$ can take such that n is a natural number is 11

$$\ \frac{\ 39+n}{4}=11$$

n = 5

The answer is option C.
I hope it helps!