Nitu has an initial capital of ₹20,000. Out of this, she invests ₹8,000 at 5.5% in Bank A, ₹5,000 at 5.6% in Bank B, and the remaining amount at $$ x\% $$ in Bank C, each rate being simple interest per annum. Her combined annual interest income from these investments equals 5% of the initial capital. If she had invested her entire initial capital in Bank C alone, what would her annual interest income (in rupees) have been?

Question

Accepted Answer

1. **Initial Setup and Combined Interest Calculation:**  
   - Initial capital = ₹20,000.  
   - Investments:  
     - Bank A = ₹8,000 at 5.5%.  
     - Bank B = ₹5,000 at 5.6%.  
     - Bank C = Remaining amount = ₹20,000 - (₹8,000 + ₹5,000) = ₹7,000 at $$ x\% $$.  
   - Combined annual interest income = $$ 5\% $$ of initial capital:  
     $$
     	ext{Combined Interest} = 0.05 	imes 20,000 = ₹1,000.
     $$

2. **Interest from Banks A and B:**  
   - Interest from Bank A:  
     $$
     	ext{Interest}_A = 8,000 	imes 0.055 = ₹440.
     $$  
   - Interest from Bank B:  
     $$
     	ext{Interest}_B = 5,000 	imes 0.056 = ₹280.
     $$

3. **Remaining Interest for Bank C:**  
   - Total interest from A and B: $$ ₹440 + ₹280 = ₹720 $$.  
   - Remaining interest for Bank C:  
     $$
     	ext{Interest}_C = 1,000 - 720 = ₹280.
     $$

4. **Rate of Interest for Bank C ($$ x\% $$):**  
   - Using simple interest formula:  
     $$
     	ext{Rate}_C = \frac{	ext{Interest}_C}{	ext{Investment}_C} 	imes 100 = \frac{280}{7,000} 	imes 100 = 4\%.
     $$

5. **If Entire Capital Was Invested in Bank C:**  
   - Annual interest income if all ₹20,000 was invested in Bank C at $$ 4\% $$:  
     $$
     	ext{Interest} = 20,000 	imes 0.04 = ₹800.
     $$

Thus, the annual interest income would have been **₹800**, and the correct answer is **D**.

Answer

Answer

Answer