a person has 50000 rupees which he wants to invest in two parts such that total annual interest at 10% on the first part and 12% on the second part amount to rupees , 5600 use Matrix multiplied to find the amount to be invested in each part
Hello,
The answer to your question will be solved in the following manner:
Lets assume that the person invests "x" amount in the first part, then the remaining amount will be "50000- x" since the whole amount is 50000. Now we have investment amounts for both parts i.e. "x" for the first part and "50000- x" for the second part.
We know that the interest rates on the respective parts are 10% and 12%. So that will amount to 0.1 and 0.12 respectively.
The total amount of interest should result in 5600 so we have to form matrix in such a way that at the end of the year we get 5600 interest rate from 50000 invested.
The answer will be as follows: M
Matrix A = [x 50000- x]
Matrix B = [0.1
0.12]
Solving the matrix we get
[x 50000-x ] * [0.1 = 5600
0.12]
[x * 0.1+ (50000-x)*0.12] = 5600
0.1x + 6000- 0.12x = 5600
0.02x = 400
x = 20000
Therefore the investment in first part will be20000 and investment in second part will be 50000-20000=30000.
Final answer will be 20000 and 30000 .
Hope it helps!
