A person invested some amount at the rate of 8 % Simple interest and the remaining some other amount at the rate of 6% simple interest he received yearly interest of ₹500 but if he had interchanged the amount invested he would received ₹50 more as interest how much amount did he invest at different rates
Answers
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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