A certain sum (in ₹)is invested at simple interest at y% per annum for at $$3\frac{1}{2}$$ years. Had it been invested at (y + 4) % per annum at simple interest, it would have fetched ₹4,452 more as interest. What is the sum?

A sum be = $$Rs  x$$

Given that , T = $$3\dfrac {1}{2} year =\dfrac {7}{2}  year $$

R = $$y % per annual $$ 

formula Simple intrest = $$\dfrac{P R T}{100}$$ (where p is principle R = rate, and T = time )

Case (1)  Simple intrest = $$ \dfrac {x \times y \times \dfrac {7}{2}} {100}$$

 $$\Rightarrow \dfrac{7xy}{200} $$

case (2) given that P = $$x$$ , T=$$\dfrac{7}{2}$$ , R = $$(y + 4)$$ % 

so Simple intrest = $$\dfrac {x \times (y+4) \times \dfrac{7}{2}}{100} $$

$$\Rightarrow \dfrac{7x \times (y+4)}{200} $$

According to question $$\dfrac {7x(y+4)}{200} - \dfrac{7xy}{200} = 4452 $$

$$\Rightarrow \dfrac {7xy}{200} +\dfrac{28x}{200} -\dfrac{7xy}{200} = 4452$$

$$\Rightarrow x = \dfrac{4452\times 200}{28} $$

$$\Rightarrow x = Rs  31800 $$ Ans