A certain sum becomes Rs. 840 in 3 years and Rs. 1200 in 7 years at simple interset. What is the value (in Rs) of the principal ?

Options

A. 520
B. 570
C. 620
D. 670

Answer

To find the principal amount based on the given information, we can follow these steps:

### Step 1: Understand the Information Given
We know that:
- The amount becomes Rs. 840 in 3 years.
- The amount becomes Rs. 1200 in 7 years.

### Step 2: Calculate the Increase in Amount
To find out how much the amount increased from 3 years to 7 years:
\[ \text{Increase} = \text{Amount after 7 years} - \text{Amount after 3 years} \]
\[ \text{Increase} = 1200 - 840 = 360 \text{ Rs.} \]

### Step 3: Determine the Time Period for the Increase
The time period between 3 years and 7 years is:
\[ 7 \text{ years} - 3 \text{ years} = 4 \text{ years} \]

### Step 4: Calculate the Interest for 4 Years
The interest earned over these 4 years is Rs. 360. Therefore, the interest per year can be calculated as:
\[ \text{Interest per year} = \frac{\text{Total Interest}}{\text{Number of Years}} \]
\[ \text{Interest per year} = \frac{360}{4} = 90 \text{ Rs.} \]

### Step 5: Calculate the Total Interest for the First 3 Years
Now, we can find the total interest earned in the first 3 years:
\[ \text{Total Interest for 3 years} = \text{Interest per year} \times 3 \]
\[ \text{Total Interest for 3 years} = 90 \times 3 = 270 \text{ Rs.} \]

### Step 6: Calculate the Principal Amount
To find the principal, we subtract the total interest earned in the first 3 years from the amount after 3 years:
\[ \text{Principal} = \text{Amount after 3 years} - \text{Total Interest for 3 years} \]
\[ \text{Principal} = 840 - 270 = 570 \text{ Rs.} \]

### Final Answer
The value of the principal is Rs. 570.

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