A cetain sum become Rs. 1020 In 5 years and Rs. 1200 in 8 years at simple interest.What is the value of principal ?

Options

A. Rs 820
B. Rs. 780
C. Rs. 700
D. Rs. 720

Answer

To find the value of the principal amount, we can use the information given about the amounts after certain years and the concept of simple interest. Here’s a step-by-step solution:

### Step 1: Understand the given information
We know that:
- The amount after 5 years is Rs. 1020.
- The amount after 8 years is Rs. 1200.

### Step 2: Calculate the interest earned in the 3 years between 5 and 8 years
The interest earned from year 5 to year 8 can be calculated as:
\[ \text{Interest for 3 years} = \text{Amount after 8 years} - \text{Amount after 5 years} \]
\[ \text{Interest for 3 years} = 1200 - 1020 = 180 \]

### Step 3: Calculate the annual interest
Since the interest earned in 3 years is Rs. 180, we can find the annual interest (SI) by dividing this amount by 3:
\[ \text{Annual Interest} = \frac{180}{3} = 60 \]

### Step 4: Calculate the total interest earned in 5 years
Now, we can calculate the total interest earned in 5 years:
\[ \text{Total Interest for 5 years} = \text{Annual Interest} \times 5 = 60 \times 5 = 300 \]

### Step 5: Calculate the principal amount
Now that we have the total interest earned in 5 years, we can find the principal amount using the amount after 5 years:
\[ \text{Principal} = \text{Amount after 5 years} - \text{Total Interest for 5 years} \]
\[ \text{Principal} = 1020 - 300 = 720 \]

### Conclusion
The value of the principal is Rs. 720.

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