A sum amounts to ₹3605 in 2019 days at 5% per annum simple interest. The sum is

Options

A. `₹3250`
B. `₹3500`
C. `₹3400`
D. `₹3550`

Answer

To find the principal sum (P) that amounts to ₹3605 in 2019 days at a rate of 5% per annum simple interest, we can follow these steps:

### Step 1: Understand the formula for Simple Interest
The formula for calculating Simple Interest (SI) is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]
Where:
- \( P \) = Principal amount
- \( R \) = Rate of interest per annum
- \( T \) = Time in years

### Step 2: Convert the time from days to years
Given that the time is 2019 days, we need to convert this into years. Since 1 year = 365 days, we can calculate:
\[ T = \frac{2019 \text{ days}}{365 \text{ days/year}} \]
\[ T \approx 5.53 \text{ years} \]

### Step 3: Calculate the Simple Interest
We know the total amount (A) is given by:
\[ A = P + \text{SI} \]
We can rearrange this to find the Simple Interest:
\[ \text{SI} = A - P \]
Substituting the values we have:
\[ \text{SI} = 3605 - P \]

### Step 4: Substitute SI in the Simple Interest formula
Now, we substitute the expression for SI into the Simple Interest formula:
\[ 3605 - P = \frac{P \times 5 \times 2019}{100 \times 365} \]

### Step 5: Simplify the equation
To simplify, first calculate the right-hand side:
\[ \frac{5 \times 2019}{100 \times 365} = \frac{10095}{36500} \approx 0.2767 \]
Now the equation becomes:
\[ 3605 - P = P \times 0.2767 \]

### Step 6: Rearrange the equation
Rearranging gives:
\[ 3605 = P + P \times 0.2767 \]
\[ 3605 = P(1 + 0.2767) \]
\[ 3605 = P \times 1.2767 \]

### Step 7: Solve for P
Now, divide both sides by 1.2767 to find P:
\[ P = \frac{3605}{1.2767} \]
Calculating this gives:
\[ P \approx 2824.00 \]

### Conclusion
The principal sum is approximately ₹2824.

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