Susan invested a certain amount of money in two schemes A and B, which offers interest at the rate of 8% per annum and 9% per annum respectively. She received Rs.1860 as annual interest. However, had she interchanged the amount of investments in the two schemes, she would have received Rs.20 more as annual interest. How much did she invest in each scheme?a.Rs.13000 in scheme A, Rs.12000 in scheme Bb.Rs.12000 in scheme A, Rs.10000 in scheme Bc.Rs.11000 in scheme A, Rs.10000 in scheme Bd.Rs.10000 in scheme A, Rs.13000 in scheme B

Let the amount invested in scheme A be Rs. x and in scheme B be Rs. y.

According to the given conditions:

The interest received from scheme A is 8% of x, which is (8/100) * x = 0.08x.
The interest received from scheme B is 9% of y, which is (9/100) * y = 0.09y.
The total interest received from both schemes is Rs. 1860, so we have the equation: 0.08x + 0.09y = 1860.
Next, if Susan had interchanged the investments in the two schemes:

The interest from scheme A would now be 9% of x, which is (9/100) * x = 0.09x.
The interest from scheme B would now be 8% of y, which is (8/100) * y = 0.08y.
The total interest in this case is Rs. 1880 (since it is Rs. 20 more than the previous interest), so we have the equation: 0.09x + 0.08y = 1880.
Now, we have the system of equations:

0.08x + 0.09y = 1860
0.09x + 0.08y = 1880
We can solve these two equations simultaneously.

Step 1: Multiply the first equation by 100 to eliminate the decimals: 8x + 9y = 186000.

Step 2: Multiply the second equation by 100 to eliminate the decimals: 9x + 8y = 188000.

Step 3: Now subtract the first equation from the second: (9x + 8y) - (8x + 9y) = 188000 - 186000 x - y = 2000.

Step 4: Solve for x: x = y + 2000.

Step 5: Substitute this value of x in the first equation: 8(x) + 9(y) = 186000 8(y + 2000) + 9y = 186000 8y + 16000 + 9y = 186000 17y + 16000 = 186000 17y = 170000 y = 170000 / 17 y = 10000.

Step 6: Now substitute the value of y in the equation x = y + 2000: x = 10000 + 2000 = 12000.

Thus, Susan invested Rs. 12000 in scheme A and Rs. 10000 in scheme B.

The correct answer is option b: Rs. 12000 in scheme A, Rs. 10000 in scheme B.