A certain sum becomes Rs. 2400 in 10 years at the rate of 2% per annum under simple interest. Find the sum.

Answer

To solve the problem step by step, we need to find the principal amount (P) that becomes Rs. 2400 in 10 years at a rate of 2% per annum under simple interest.

### Step-by-step Solution:

1. **Identify the given values**:
- Amount (A) = Rs. 2400
- Time (T) = 10 years
- Rate (R) = 2% per annum

2. **Recall the formula for the amount in simple interest**:
\[ A = P + SI \]
where \( SI \) (Simple Interest) is given by:
\[ SI = \frac{P \times R \times T}{100} \]
Therefore, we can rewrite the amount formula as:
\[ A = P + \frac{P \times R \times T}{100} \]

3. **Substituting the known values into the formula**:
\[ 2400 = P + \frac{P \times 2 \times 10}{100} \]

4. **Simplify the equation**:
\[ 2400 = P + \frac{20P}{100} \]
\[ 2400 = P + \frac{P}{5} \]
(since \( \frac{20}{100} = \frac{1}{5} \))

5. **Combine the terms on the right side**:
\[ 2400 = P + 0.2P \]
\[ 2400 = 1.2P \]

6. **Solve for P**:
\[ P = \frac{2400}{1.2} \]
\[ P = 2000 \]

7. **Conclusion**:
The principal amount is Rs. 2000.