A person invested some amount at …

Suppose that he invested ₹ x at the rate of 12% simple interest and ₹ y at the rate 10% simple interest.
Then, according to the question,{tex}\frac{12x}{{100}} + \frac{{10y}}{{100}} = 130{/tex}
{tex}\Rightarrow {/tex} 12x+10y=13000 ..........Dividing throughout by 2
{tex}\Rightarrow {/tex} 6x+5y=6500 .......(1)
and,{tex}\frac{{12y}}{{100}} + \frac{{10x}}{{100}} = 134 {/tex}
{tex}\Rightarrow {/tex} 12y+10x=13400
{tex}\Rightarrow {/tex} 6y+5x=6700 .............Dividing through by 2
{tex}\Rightarrow {/tex} 5x+6y=6700  ...........(2)

Multiplying equation (1) by 6 and equation (2) by 5, we get
36x+30y=39000  ...............(3)
25x+30y=33500 .......(4)
{tex}\Rightarrow {/tex}subtracting (3) and (4) we get x = 500
Substituting this value of x in equation (1), we get 6(500)+5y=6500
{tex}\Rightarrow {/tex} 3000+5y=6500
{tex}\Rightarrow {/tex} 5y=6500-3000
{tex}\Rightarrow {/tex} 5y=3500
{tex}\Rightarrow {/tex} {tex}y = \frac{{3500}}{5} = 700{/tex}

So, the solution of the equation (1) and (2) is x=500 and y=700
Hence, he invested ₹ 500 at the rate of 12% simple interest and ₹ 700 at the rate of 10% simple interest.
verification.Substituting x=500, y=700,
We find that both the equation (1) and (2) are satisfied as shown below:
6x + 5y=6(500)+5(700)=3000+3500=6500
5x+6y=5(500)+6(700)=2500+4200=6700
This verifies the solution.