Mr. Pinto invests one-fifth of his capital at 6%, one-third at 10% and the remaining at 1%, each rate being simple interest per annum. Then, the minimum number of years required for the cumulative interest income from these investments to equal or exceed his initial capital is

Question

Accepted Answer

Let Mr. Pinto's initial capital be ₹300 (chosen for ease of calculation as it is divisible by both 5 and 3).

### Step-by-Step Calculation:
1. **Capital Distribution:**  
   - One-fifth of ₹300 is ₹60, invested at 6%.  
   - One-third of ₹300 is ₹100, invested at 10%.  
   - Remaining amount is ₹140, invested at 1%.

2. **Yearly Interest Calculation:**  
   - Interest from ₹60 at 6%: $$60 	imes \frac{6}{100} = ₹3.6$$ per year.  
   - Interest from ₹100 at 10%: $$100 	imes \frac{10}{100} = ₹10$$ per year.  
   - Interest from ₹140 at 1%: $$140 	imes \frac{1}{100} = ₹1.4$$ per year.

Total yearly interest = $$₹3.6 + ₹10 + ₹1.4 = ₹15$$ per year.

3. **Finding Minimum Years:**  
   To determine the number of years required for the cumulative interest to equal or exceed the capital:  
   $$
   	ext{Total Interest} = 	ext{Yearly Interest} 	imes n
   $$
   For the cumulative interest to equal the capital:  
   $$
   ₹15 	imes n = ₹300
   $$
   Solve for $$n$$:  
   $$
   n = \frac{300}{15} = 20
   $$

Thus, the minimum number of years required is **20 years**.