A certain sum of money amounts to ₹8,928 in twoyears and to ₹10,224 in $$3\frac{1}{2}$$ years, both at simple interest. The rate of interest per annum is:

We know that formula simple interest (S I) = $$\dfrac{PRT}{100} $$ and A =  P + SI 

Case (1)   $$ 8928 = P + \dfrac{PR2}{100} $$  ........... equestion(1)

Case (2    $$ 10224 = P + \dfrac { PR 3.5} {100}$$ ........ equestion (2)

Divide  equestion (2) by equestion (1)

$$\dfrac {10224}{8928} = \dfrac {100 + 3.5R}{100 +2R} $$

$$\Rightarrow 8928 \times (100 + 3.5) = 10224 \times (100 + 2R)$$

$$\Rightarrow R = \dfrac{1296 \times100}{10800}$$

$$\Rightarrow R = 12  $$%Ans