The difference between the compound interest and simple interest on ₹ x at 8.5% per annum for 2 years is ₹ 28.90. The value of x is:

Given that,

Rate of interest $$=8.5\%$$ per annum

time$$=2$$ years

difference between the compound interest and simple interest $$=28.90$$ Rs.

Principle amount=x,

Now, we know that simple interest (SI)$$=\dfrac{P\times R\times t}{100}$$

Substituting the values,

$$SI=\dfrac{x\times 8.5 \times 2}{100}$$

$$\Rightarrow SI=\dfrac{x \times 8.5 \times 2}{100}-------(i)$$

Now, for compound interest Final amount$$(A)=P(1+\dfrac{R}{100})^t$$

Now substituting the values, $$A=x(1+\dfrac{8.5}{100})^2$$

$$\Rightarrow A=x(1.085)^2$$

$$\Rightarrow A=x(1.085)^2$$

$$\Rightarrow A=1.1772x $$

Hence compound interest $$CI= A-P=1.177x-x=0.1772x--------(ii)$$

From equation(i) and (ii)

$$CI-SI=28.90$$

$$\Rightarrow 0.170x-0.177x=28.90$$

$$\Rightarrow 0.007x=28.90$$

$$\Rightarrow x=\dfrac{28.90}{0.007}=4128$$Rs.

Option will be the correct answer because it's the nearest value.