In simple interest rate per annum a certain sum amounts to₹5046.6 in 2 years and ₹ 5628.9 in 3 years. The principal in rupees is
कोई धन राशि साधारण ब्याज की वार्षिक दर पर 2 वर्ष में ₹ 5046.6 और 3 वर्ष में ₹ 5628.9 हो जाती है। ₹ में मूलधन बताइए ?

Options

A. ₹ 2882
B. ₹5000
C. ₹3882
D. ₹4000

Answer

To find the principal amount based on the given simple interest amounts, we can follow these steps:

### Step 1: Identify the amounts after 2 and 3 years
- Amount after 2 years (A2) = ₹5046.6
- Amount after 3 years (A3) = ₹5628.9

### Step 2: Calculate the interest for 1 year
The interest for 1 year can be found by subtracting the amount after 2 years from the amount after 3 years:
\[ \text{Interest for 1 year} = A3 - A2 = 5628.9 - 5046.6 = ₹582.3 \]

### Step 3: Calculate the total interest for 2 years
Since we know the interest for 1 year, we can calculate the total interest for 2 years:
\[ \text{Total Interest for 2 years} = \text{Interest for 1 year} \times 2 = 582.3 \times 2 = ₹1164.6 \]

### Step 4: Use the amount after 2 years to find the principal
The amount after 2 years is the sum of the principal and the total interest for 2 years:
\[ A2 = \text{Principal} + \text{Total Interest for 2 years} \]
Rearranging this gives us:
\[ \text{Principal} = A2 - \text{Total Interest for 2 years} \]
Substituting the values:
\[ \text{Principal} = 5046.6 - 1164.6 = ₹3882 \]

### Final Answer
The principal amount is ₹3882.

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