Question

13. A person invests some amount @ 12% S.I. and some other amount @ 10% S.I..He receives an annual
interest of Rs. 1300. But if he interchanges the amounts invested, he shall receive Rs.40 more as interest.
How much has he invested at each rate?​

Answer 1

Answer:

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.

I hope my answer helps uh out!!