Question

Question : A person invested some money at 12% sample interest and some other at 10% simple interest. He received yearly interest of ₹1300. If he had interchanged the amounts, he would have received ₹40 more as yearly interest. How much did he invest at different rates?

So, the equations are :
6x + 5y = 13000
5x + 6y = 13400

Coefficients equated to :
30x + 25y = 65000
30x + 36y = 80400

Subtracted to :
-11y = -15400
y = 1400
x = 1000

How do i calculate the investment then?
Please also correct my steps if they're wrong

ty <3​​

Answer 1

Step-by-step explanation:

Suppose the person invested Rs x at the rate of 12% simple interest and Rs y at the rate of 10% simple interest. Then,

Yearly interest =

100

12x

+

100

10y

∴

100

12x

+

100

10y

=130

⇒12x+10y=13000

⇒6x+5y=6500 .(i)

In the invested amounts are interchanged, then yearly interest increased by Rs 4.

∴

100

10x

+

100

12y

=134

⇒10x+12y=13400

⇒5x+6y=6700 ..(ii)

Subtracting equation (ii) from equation (i), we get

x−y=−200 .(iii)

Adding equation (ii) and (i), we get

11x+11y=13200

⇒x+y=1200 ..(iv)

Adding equations (iii) and (iv), we get

2x=1000⇒x=500

Putting x=500 in equation (iii), we get y=700

Thus, the person invested Rs 500 at the rate of 12% per year and Rs 700 at the rate of 10% per year.