A person invested a sum of ₹6,500 at $$x$$% per annum at simple interest and a sum of ₹7,500 at $$\left(x - 2\right)\%$$ at simple interest. If total interest earned on both the investments for 3 years is ₹3,750. then the rate of interest on the second investment is:

Given, 

First investment :

P1 = ₹6500

R = x%

T = 3 yr

Second Investment : 

P2 = ₹7500

R = (x-2)%

Time = 3 yr

As we know , 

$$S.I\ =\ \frac{\left(P\times R\times\ T\right)}{100}$$

According to Question, 

$$\frac{\left(6500\times x\times\ 3\right)}{100}+\frac{\left(7500\times\ \left(x-2\right)\times\ 3\right)}{100}=3750$$

$$195x+225x-450=3750$$

$$420x=4200$$

x = 10 %

The rate of interest on second investment = x - 2 = 8%

Hence, Option A is correct.