If the ratio of sum of products net prices in 2015, 2016 and 2017 to products list price in 2017 is $$\left(5+\frac{1}{p}+\frac{1}{p^{2}}\right) \frac{75}{131} : 1$$ then calculate the value of P.

The question had an error in the original question paper, where the ratio $$\left(5+\frac{1}{p}+\frac{1}{p^{2}}\right) \frac{75}{131} : 1$$ was given as $$5\left(5+\frac{1}{p}+\frac{1}{p^{2}}\right) \frac{75}{131} : 1$$.

The sum of the product's net prices in 2015, 2016 and 2017 is $$7000+5000+3000=15000$$ million
The products list price in year 2017 is 5 billion, which is equivalent to 5000 million.
The ratio of the sum of net prices to the list price would be 15000:5000 = 3:1

Equating this with the ratio we are given, we get
$$\left(5+\frac{1}{p}+\frac{1}{p^2}\right)\ \frac{75}{131}:1\ =\ 3:1$$
$$\frac{\left(5p^2+p+1\right)}{p^2}\times\ \frac{75}{131}=3$$

131 is a prime number and in order to cancel it out from the denominator, we would require 131 in the numerator as well. 
At this point, we can try putting in the options to see if we can get 131 in the numberator.

putting p=5, we get $$\left(5(5)^2+(5)+1\right)$$ as 131
Using 5 as the value of p, we get:
$$\ \frac{131}{25}\times\ \frac{75}{131}=3$$

Therefore, Option C is the correct answer.