If a total of 8000 rupees invested in two different schemes offering compound interests of 10%, 12% to recieve 2600 rupees as total interest after 2years, find the amount invested at 12% scheme.

Let the amount invested in 10% scheme is x. So, amount in 12% scheme is (8000-x)
So, the total amount with interest after 2 years is 8000+2600=10600
This value should be equal to, $$x(1+10/100)^{2}+(8000-x)(1+20/100)^{2}$$
$$x(1.1)^{2}+(8000-x)(1.2)^{2}=10600$$
1.21x+8000*1.44-1.44x=10600
=> 0.23x=920
=> x=4000
So, he invested 4000 in both the schemes