A person invested some money at 12% simple interest and some other amount at 10% simple interest. He received early interest of Rs.1300. If he had interchanged the amounts, he would have received rupees Rs.40 more as yearly interest. How much did he invest at different rates?
Answers
Answer:
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. 130. But if he had interchanged the amounts invested, he would have received Rs 4 more as interest. How much amount did he invest at different rates
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.
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