A person borrows Rs 5,000 for 2 years at 4 % per annum simple interset. He immediately lends it to another person at `6 (1)/(4) %` per annum simple interset for 2 years. His gain in the transaction is

Options

A. Rs 112.50
B. Rs 450
C. Rs 225
D. Rs 150

Answer

To solve the problem step by step, we will calculate the simple interest for both transactions and then find the gain from the transaction.

### Step 1: Calculate the Simple Interest for Borrowing
The person borrows Rs 5,000 at a rate of 4% per annum for 2 years.

**Formula for Simple Interest (SI):**
\[ \text{SI} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (Rs 5,000)
- \( R \) = Rate of interest (4%)
- \( T \) = Time (2 years)

**Calculation:**
\[ \text{SI} = \frac{5000 \times 4 \times 2}{100} \]
\[ \text{SI} = \frac{40000}{100} \]
\[ \text{SI} = 400 \]

So, the interest paid for borrowing is Rs 400.

### Step 2: Calculate the Simple Interest for Lending
The person lends the same Rs 5,000 at a rate of \( 6 \frac{1}{4} \% \) per annum for 2 years. First, convert \( 6 \frac{1}{4} \% \) into an improper fraction.

**Conversion:**
\[ 6 \frac{1}{4} = \frac{25}{4} \]

Now, we will use the same formula for Simple Interest.

**Calculation:**
\[ \text{SI} = \frac{5000 \times \frac{25}{4} \times 2}{100} \]
\[ \text{SI} = \frac{5000 \times 25 \times 2}{4 \times 100} \]
\[ \text{SI} = \frac{250000}{400} \]
\[ \text{SI} = 625 \]

So, the interest received from lending is Rs 625.

### Step 3: Calculate the Gain
Now, we will find the gain from the transaction by subtracting the interest paid from the interest received.

**Calculation:**
\[ \text{Gain} = \text{Interest received} - \text{Interest paid} \]
\[ \text{Gain} = 625 - 400 \]
\[ \text{Gain} = 225 \]

Thus, the gain in the transaction is Rs 225.

### Final Answer:
The gain in the transaction is Rs 225.

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