A person invested some account at the rate of 12% simple interest and a certain amount at rate of 10% simple interest. He received yearly interest of Rs. 130. But if he had interchanged the amounts invested,he would have received Rs. 4 more as interest. How much did he invest at 12% simple interest ?

Explanation:-

Let the amount invested at 12% be Rs. x and that invested at 10% be Rs. y
$$\eqalign{ & Then, \cr & \to 12\% \,{\text{of }}x + 10\% \,{\text{of }}y = 130 \cr & \Rightarrow 12x + 10y = 13000 \cr & \Rightarrow 6x + 5y = 6500......{\text{(i)}} \cr & {\text{And,}} \cr & \to 10\% \,{\text{of }}x + 12\% \,{\text{of }}y = 134 \cr & \Rightarrow 10x + 12y = 13400 \cr & \Rightarrow 5x + 6y = 6700......{\text{(ii)}} \cr & {\text{Adding (i) and (ii), we get:}} \cr & 11\left( {x + y} \right) = 13200 \cr & \Rightarrow x + y = 1200.......({\text{iii}}) \cr & {\text{Subtracting (i) from (ii),}} \cr & {\text{we get: }} - x + y = 200.......({\text{iv}}) \cr & {\text{Adding (iii) and (iv), }} \cr & {\text{we get}}:2y = 1400\,or\,y = 700. \cr & {\text{Hence,}} \cr & {\text{Amount invested at}} \cr & 12\% = \left( {1200 - 700} \right) \cr & = {\text{Rs}}{\text{. 500}}. \cr}$$