A person invested some amount at the rate of 12% simple interest and some other amount at the rate of 10% simple interest. He received yearly interest of Rs. 1300. But if he had interchanged the amounts invested, he would have received Rs 40 more as interest. How much amount did he invest at different rates please give step by step explination
Answers
Answer:
The Cape of Good Hope is a headland on the Atlantic coast side of South Africa. ... It was later renamed, by King John II of Portugal, the Cape of Good Hope because of the great optimism engendered by the opening of a sea route to India and the East.
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.