In what time will Rs. 8100 produce the same income at 3% as Rs. 225 in 4 years at 3%.

Answer

To solve the problem step by step, we need to find out how long it will take for Rs. 8100 to produce the same income at 3% per annum as Rs. 225 does in 4 years at the same rate.

### Step 1: Calculate the income from Rs. 225 in 4 years at 3% per annum.
Using the formula for Simple Interest (SI):
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 225 \) (Principal)
- \( R = 3 \) (Rate of interest)
- \( T = 4 \) (Time in years)

Substituting the values:
\[ \text{SI} = \frac{225 \times 3 \times 4}{100} \]
\[ \text{SI} = \frac{2700}{100} = 27 \]

### Step 2: Set up the equation for Rs. 8100 to produce the same income.
We want to find the time \( T \) for Rs. 8100 to produce an interest of Rs. 27 at 3% per annum. Using the same formula for Simple Interest:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P = 8100 \)
- \( R = 3 \)
- \( \text{SI} = 27 \)

Substituting the values:
\[ 27 = \frac{8100 \times 3 \times T}{100} \]

### Step 3: Solve for \( T \).
Rearranging the equation to solve for \( T \):
\[ 27 = \frac{24300 \times T}{100} \]
Multiplying both sides by 100:
\[ 2700 = 24300 \times T \]
Now, divide both sides by 24300:
\[ T = \frac{2700}{24300} \]
Simplifying the fraction:
\[ T = \frac{1}{9} \text{ years} \]

### Step 4: Convert \( T \) into months (if needed).
Since 1 year = 12 months:
\[ T = \frac{1}{9} \times 12 = \frac{12}{9} = \frac{4}{3} \text{ months} \]

### Final Answer:
The time it will take for Rs. 8100 to produce the same income at 3% as Rs. 225 in 4 years at 3% is \( \frac{1}{9} \) years or \( \frac{4}{3} \) months.

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