Simple interest of an amount for a period of 12 years is Rs 2400. If the amount is trepled after 3 years then what is that amount?

Options

A. a)Rs 6300
B. b)Rs 7200
C. c)Rs 5600
D. d)Rs 6000

Answer

To solve the problem step by step, we will use the concept of Simple Interest (SI) and the information given in the question.

### Step 1: Understanding the Simple Interest Formula
The formula for Simple Interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(SI\) = Simple Interest
- \(P\) = Principal amount (initial amount)
- \(R\) = Rate of interest per annum
- \(T\) = Time in years

### Step 2: Given Information
From the question, we know:
- The Simple Interest for 12 years is Rs 2400.
- Therefore, \(T = 12\) years and \(SI = 2400\).

### Step 3: Calculate the Simple Interest for 1 Year
To find the Simple Interest for 1 year, we divide the total Simple Interest by the number of years:
\[ SI \text{ for 1 year} = \frac{2400}{12} = 200 \text{ Rs} \]

### Step 4: Calculate Simple Interest for the First 3 Years
For the first 3 years, the Simple Interest will be:
\[ SI \text{ for 3 years} = 200 \times 3 = 600 \text{ Rs} \]

### Step 5: Calculate Remaining Simple Interest for the Next 9 Years
After 3 years, the principal amount is tripled. Thus, the remaining Simple Interest for the next 9 years will be calculated based on the new principal amount.

The total Simple Interest for 12 years is Rs 2400, and we have already calculated Rs 600 for the first 3 years. Therefore, the Simple Interest for the next 9 years is:
\[ SI \text{ for next 9 years} = 2400 - 600 = 1800 \text{ Rs} \]

### Step 6: Tripling the Principal Amount
Since the principal amount is tripled after 3 years, the Simple Interest for the next 9 years will also be tripled:
\[ SI \text{ for next 9 years with tripled principal} = 1800 \times 3 = 5400 \text{ Rs} \]

### Step 7: Total Simple Interest for 12 Years
Now, we can calculate the total Simple Interest for the entire 12 years:
\[ \text{Total SI} = SI \text{ for first 3 years} + SI \text{ for next 9 years} \]
\[ \text{Total SI} = 600 + 5400 = 6000 \text{ Rs} \]

### Step 8: Conclusion
Thus, the total Simple Interest after 12 years is Rs 6000.

### Final Answer
The amount after 12 years is Rs 6000.

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