Sagarika divides her savings of 10000 rupees to invest across two schemes A and B. Scheme A offers an interest rate of 10% per annum, compounded half-yearly, while scheme B offers a simple interest rate of 12% per annum. If at the end of first year, the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees, then the total interest, in rupees, earned by Sagarika during the first year of investment is

Let Sagarika divide the 10,000 rupees into x and y, such that she invests x in scheme A and y in scheme B.

So x+y=10,000 ; or x=10,000-y _______(1)

Scheme A is compound interest at 10% compounded half-yearly. 

So, athe mount after 1 year will be $$A=x\left(1+\frac{5}{200}\right)^{2.1}=x\left(1.05\right)^2=1.1025x$$,

And, interest is 1.1025x-x=0.1025x

Scheme B is simple interest at 12% per annum,

So interest is $$SI=\frac{y\times\ 12\times\ 1}{100}=0.12y$$

And the amount is $$SI+P=0.12y+y=1.12y$$

Now, it is given that the value of her investment in scheme B exceeds the value of her investment in scheme A by 2310 rupees,

So, 1.12y-1.1025x=2310

or, 1.12y-1.1025(10,000-y)=2310

or, 1.12y+1.1025y-11025=2310

or,2.222y=13335

or, y=6000. so x=4000

Now, total interest = 0.12y+0.1025x=1130, which is the answer.