Question

Hari invested an amount at a certain rate of interest on simple interest and he got 60% more amount after 8 years. If he invests Rs. 9600 at the same rate of interest on simple interest then find the total interest he would get after four years.

• A. Rs. 2520
• B. Rs. 2260
• C. Rs. 2880
• D. Rs. 2160

Hint:

For simple interest, use the formula \( \text{SI} = \frac{P \times R \times T}{100} \) and make sure to adjust the rate and time accordingly.

Answer 1

The Correct Option is C

Step 1: Understand the problem. 
Let the principal be \( P \), and the rate of interest be \( R % \) per annum. The total amount after 8 years is 60% more than the principal, so: 
\[ A = P + \text{SI} = P\left(1 + \frac{R \times T}{100}\right). \] After 8 years, the total amount is 60% more than the principal: 
\[ A = 1.60P. \]

Step 2: Find the rate of interest. 
Using the formula for simple interest: 
\[ A = P \left(1 + \frac{R \times T}{100}\right) \Rightarrow 1.60P = P \left(1 + \frac{R \times 8}{100}\right). \] Dividing both sides by \( P \): 
\[ 1.60 = 1 + \frac{8R}{100}. \] Simplifying this equation: 
\[ 0.60 = \frac{8R}{100} \Rightarrow R = \frac{0.60 \times 100}{8} = 7.5%. \]

Step 3: Calculate the interest for Rs. 9600 after 4 years. 
Now that we know the rate of interest is 7.5%, we can calculate the interest for Rs. 9600 for 4 years: 
\[ \text{SI} = \frac{P \times R \times T}{100} = \frac{9600 \times 7.5 \times 4}{100} = 2880. \]

Step 4: Conclusion. 
Thus, the total interest he would get after four years is Rs. 2880, and the correct answer is (c).