Find the sum, invested at 10% compounded annually, on which the interest for the third year exceeds the interest of the first year by रु 252.

Explanation

To find the sum invested at 10% compounded annually, where the interest for the third year exceeds the interest of the first year by ₹252, we can follow these steps:

### Step 1: Define the Principal Amount
Let the principal amount be \( P \).

### Step 2: Calculate Interest for the First Year
The interest for the first year \( I_1 \) can be calculated as:
\[ I_1 = \frac{10}{100} \times P = 0.1P \]

### Step 3: Calculate the Amount After the First Year
The amount after the first year \( A_1 \) is:
\[ A_1 = P + I_1 = P + 0.1P = 1.1P \]

### Step 4: Calculate Interest for the Second Year
The interest for the second year \( I_2 \) is calculated on the amount after the first year:
\[ I_2 = \frac{10}{100} \times A_1 = \frac{10}{100} \times 1.1P = 0.11P \]

### Step 5: Calculate the Amount After the Second Year
The amount after the second year \( A_2 \) is:
\[ A_2 = A_1 + I_2 = 1.1P + 0.11P = 1.21P \]

### Step 6: Calculate Interest for the Third Year
The interest for the third year \( I_3 \) is calculated on the amount after the second year:
\[ I_3 = \frac{10}{100} \times A_2 = \frac{10}{100} \times 1.21P = 0.121P \]

### Step 7: Set Up the Equation for the Difference in Interest
According to the problem, the interest for the third year exceeds the interest of the first year by ₹252:
\[ I_3 - I_1 = 252 \]
Substituting the values we calculated:
\[ 0.121P - 0.1P = 252 \]
\[ 0.021P = 252 \]

### Step 8: Solve for the Principal Amount \( P \)
To find \( P \), we divide both sides by 0.021:
\[ P = \frac{252}{0.021} \]
Calculating this gives:
\[ P = 12000 \]

### Final Answer
The principal amount invested is ₹12,000.

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