A certain amount was invested for certain time and at a certain rate at simple interest. After 2 years, amount obtained is Rs.24000 and after 5 years total amount obtained Rs.30000. Find the amount invested initially,

Options

A. Rs.25000
B. Rs.20000
C. Rs.40000
D. Rs.30000

Answer

To solve the problem, we need to determine the initial amount invested based on the information provided about the total amounts after 2 years and 5 years.

### Step-by-Step Solution:

1. **Identify the amounts after given years:**
- After 2 years, the total amount (A) is Rs. 24,000.
- After 5 years, the total amount (A) is Rs. 30,000.

2. **Calculate the increase in amount over the 3 years (from year 2 to year 5):**
- Increase = Amount after 5 years - Amount after 2 years
- Increase = Rs. 30,000 - Rs. 24,000 = Rs. 6,000

3. **Determine the annual interest earned:**
- Since this increase of Rs. 6,000 occurred over 3 years, we can find the annual interest.
- Annual Interest = Increase / Number of years
- Annual Interest = Rs. 6,000 / 3 = Rs. 2,000

4. **Calculate the total interest earned in the first 2 years:**
- Total Interest for 2 years = Annual Interest × Number of years
- Total Interest for 2 years = Rs. 2,000 × 2 = Rs. 4,000

5. **Find the initial amount invested:**
- We know that after 2 years, the total amount is Rs. 24,000, which includes the initial amount (P) and the interest earned in 2 years.
- Therefore, we can set up the equation:
\[ P + \text{Total Interest for 2 years} = 24,000 \]
- Substituting the value of Total Interest:
\[ P + 4,000 = 24,000 \]
- Now, solve for P:
\[ P = 24,000 - 4,000 = 20,000 \]

6. **Conclusion:**
- The initial amount invested is Rs. 20,000.

### Final Answer:
The amount invested initially is Rs. 20,000.