The simple interest on a sum of money will be X 200 after 5 yr. In the next 5 yr, principal is tripled. What will be the total interest at the end of the 10th yr?

Options

A. 650
B. 850
C. 800
D. 750

Answer

To solve the problem step by step, we will calculate the simple interest for the first 5 years and then for the next 5 years when the principal is tripled.

### Step 1: Calculate the Simple Interest for the First 5 Years
The simple interest (SI) for the first 5 years is given as 200.

**Formula for Simple Interest:**
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

From the problem, we know:
\[ \text{SI} = 200 \]
\[ T = 5 \text{ years} \]

### Step 2: Calculate the Simple Interest for the Next 5 Years
After 5 years, the principal is tripled. Therefore, the new principal \( P' \) becomes:
\[ P' = 3P \]

Since the rate of interest and time remain the same, the simple interest for the next 5 years will also be calculated using the same formula:
\[ \text{SI for next 5 years} = \frac{P' \times R \times T}{100} = \frac{3P \times R \times 5}{100} \]

### Step 3: Relate the Simple Interest for the Next 5 Years to the First 5 Years
Since we know that the simple interest for the first 5 years is 200, we can express the simple interest for the next 5 years as:
\[ \text{SI for next 5 years} = 3 \times \text{SI for first 5 years} = 3 \times 200 = 600 \]

### Step 4: Calculate the Total Simple Interest at the End of 10 Years
Now, we can find the total simple interest over the 10 years by adding the simple interest from the first 5 years and the next 5 years:
\[ \text{Total SI} = \text{SI for first 5 years} + \text{SI for next 5 years} \]
\[ \text{Total SI} = 200 + 600 = 800 \]

### Final Answer
The total interest at the end of the 10th year is **800**.

---