A person invested a sum of Rs. 10,500 at x% per annum at simple interest and a sum of Rs. 13,500 at (x + 2)% p.a. at simple interest. If the total interest earned on both the investments for 3 years is Rs. 7,650, then the rate of interest on the first investment is:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 9.5%
Simple interest is \(\displaystyle\frac{P\times R\times T}{100}\); the interest of the two investments for 3 years adds up to Rs. 7,650.
First investment: \(\displaystyle\frac{10500\times x\times3}{100}=315x\)
Second investment: \(\displaystyle\frac{13500\times(x+2)\times3}{100}=405(x+2)=405x+810\)
Total interest of both investments: \(315x+405x+810=7650\)
\(720x=6840\)
\(x=9.5\), so the rate on the first investment is 9.5% per annum