Question : A person invested a sum of INR 10,500 at $x$% per annum at simple interest and a sum of INR 13,500 at $(x + 2)$% p.a. at simple interest. If the total interest earned on both investments for 3 years is INR 7,650, then the rate of interest on the first investment is:
Option 1: 8%
Option 2: 8.5%
Option 3: 9%
Option 4: 9.5%
Correct Answer: 9.5%
Solution :
Given: 1st principal = INR 10,500
Rate of interest = $x$%
2nd principal = INR 13,500
Rate of interest = $(x + 2)$%
Time = 3 years
The total simple interest = INR 7,650
We know that,
Simple interest = $\frac{\text{Principal × Rate × Time}}{100}$
⇒ $7650 = \frac{10500\times x\times3}{100}+ \frac{13500\times (x+2)\times3}{100}$
⇒ $7650 = 315x+ 405x+810$
⇒ $6840 = 720x$
⇒ $x=\frac{6840}{720}= 9.5$
Hence, the correct answer is 9.5%.
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