On what date will Rs. 1,950 lent on 5th January, 2011 amount to Rs. `2,125*50` at 5 per cent per annum simple interest ?

Answer

To solve the problem step by step, we will follow the process of calculating the simple interest, determining the time period, and then finding the final date when the amount will be repaid.

### Step 1: Identify the Given Values
- Principal (P) = Rs. 1,950
- Amount (A) = Rs. 2,125.50
- Rate (R) = 5% per annum

### Step 2: Calculate the Simple Interest (SI)
The formula for Simple Interest is:
\[ \text{SI} = A - P \]

Substituting the values:
\[ \text{SI} = 2,125.50 - 1,950 \]
\[ \text{SI} = 175.50 \]

### Step 3: Use the Simple Interest Formula to Find Time (T)
The formula for Simple Interest is also given by:
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Rearranging the formula to solve for T:
\[ T = \frac{\text{SI} \times 100}{P \times R} \]

Substituting the known values:
\[ T = \frac{175.50 \times 100}{1,950 \times 5} \]

Calculating the denominator:
\[ 1,950 \times 5 = 9,750 \]

Now substituting this back into the equation:
\[ T = \frac{175.50 \times 100}{9,750} \]
\[ T = \frac{17,550}{9,750} \]
\[ T = 1.8 \text{ years} \]

### Step 4: Convert Time into Years and Days
1.8 years can be expressed as:
- 1 year and 0.8 years.

To convert 0.8 years into days:
\[ 0.8 \times 365 = 292 \text{ days} \]

### Step 5: Determine the Final Date
The principal was lent on **5th January 2011**. We need to add 1 year and 292 days to this date.

1. **Adding 1 year:**
- 5th January 2011 + 1 year = 5th January 2012

2. **Adding 292 days to 5th January 2012:**
- January has 31 days, so from 5th January to 31st January is:
\[ 31 - 5 = 26 \text{ days} \]
- Remaining days to add:
\[ 292 - 26 = 266 \text{ days} \]

- February 2012 (leap year) has 29 days:
\[ 266 - 29 = 237 \text{ days} \]

- March has 31 days:
\[ 237 - 31 = 206 \text{ days} \]

- April has 30 days:
\[ 206 - 30 = 176 \text{ days} \]

- May has 31 days:
\[ 176 - 31 = 145 \text{ days} \]

- June has 30 days:
\[ 145 - 30 = 115 \text{ days} \]

- July has 31 days:
\[ 115 - 31 = 84 \text{ days} \]

- August has 31 days:
\[ 84 - 31 = 53 \text{ days} \]

- September has 30 days:
\[ 53 - 30 = 23 \text{ days} \]

- October has 31 days, so we can add the remaining 23 days:
- Thus, we reach **23rd October 2012**.

### Final Answer
The amount of Rs. 1,950 will amount to Rs. 2,125.50 on **23rd October 2012**.

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