The simple interest on a sum of money will be rupees 210 after 3 years. In the next 3 years.principal becomes 4 times.then the total interest at the end of 6 years.

Options

A. 1020
B. 1050
C. 1080
D. 1100

Explanation

To solve the problem step by step, we will follow the details provided in the video transcript.

### Step 1: Understand the given information
We know that the simple interest (SI) on a sum of money is Rs 210 after 3 years.

### Step 2: Use the formula for Simple Interest
The formula for simple interest is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \( SI \) = Simple Interest
- \( P \) = Principal amount
- \( R \) = Rate of interest (per annum)
- \( T \) = Time (in years)

### Step 3: Set up the equation for the first 3 years
From the information given:
\[ \frac{P \times R \times 3}{100} = 210 \]
This can be rearranged to:
\[ P \times R = \frac{210 \times 100}{3} = 7000 \tag{1} \]

### Step 4: Analyze the next 3 years
In the next 3 years, the principal becomes 4 times the original principal. Therefore, the new principal is:
\[ 4P \]
The time for this period is still 3 years.

### Step 5: Set up the equation for the next 3 years
Using the simple interest formula again for the next 3 years:
\[ SI_{next} = \frac{4P \times R \times 3}{100} \]
This can be simplified to:
\[ SI_{next} = 4 \times \frac{P \times R \times 3}{100} = 4 \times 210 = 840 \tag{2} \]

### Step 6: Calculate the total interest for 6 years
The total interest at the end of 6 years is the sum of the interest from the first 3 years and the interest from the next 3 years:
\[ Total\ Interest = SI_{first\ 3\ years} + SI_{next\ 3\ years} \]
Substituting the values from equations (1) and (2):
\[ Total\ Interest = 210 + 840 = 1050 \]

### Final Answer
The total interest at the end of 6 years is Rs 1050.

---