A person borrows Rs. 5000 for 2 years at 4% p.a. simple interest. He immediately lents it to another person at `6(1)/(4)%` p.a. for 2 years. Find his gain in the transaction per year.

Options

A. Rs 112.50
B. Rs. 125
C. Rs. 150
D. Rs. 167.50

Answer

To solve the problem step-by-step, we will calculate the simple interest for both the borrowing and lending transactions, and then find the gain per year.

### Step 1: Calculate the Simple Interest for Borrowing
The formula for Simple Interest (SI) is:
\[ SI = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount (Rs. 5000)
- \(R\) = Rate of interest (4% per annum)
- \(T\) = Time (2 years)

Substituting the values:
\[ SI_{borrowed} = \frac{5000 \times 4 \times 2}{100} \]
Calculating this:
\[ SI_{borrowed} = \frac{5000 \times 8}{100} = \frac{40000}{100} = 400 \text{ Rs.} \]

### Step 2: Calculate the Simple Interest for Lending
Now, we calculate the simple interest for the amount lent at a rate of \(6\frac{1}{4}\%\) per annum. First, convert \(6\frac{1}{4}\%\) to a fraction:
\[ 6\frac{1}{4}\% = \frac{25}{4}\% \]

Using the same formula for Simple Interest:
\[ SI_{lent} = \frac{P \times R \times T}{100} \]
Where:
- \(P\) = Principal amount (Rs. 5000)
- \(R\) = Rate of interest (\(\frac{25}{4}\%\))
- \(T\) = Time (2 years)

Substituting the values:
\[ SI_{lent} = \frac{5000 \times \frac{25}{4} \times 2}{100} \]
Calculating this:
\[ SI_{lent} = \frac{5000 \times 25 \times 2}{4 \times 100} = \frac{250000}{400} = 625 \text{ Rs.} \]

### Step 3: Calculate the Gain from the Transaction
Now, we find the gain from the transaction:
\[ \text{Gain} = SI_{lent} - SI_{borrowed} \]
Substituting the values:
\[ \text{Gain} = 625 - 400 = 225 \text{ Rs.} \]

### Step 4: Calculate the Gain per Year
To find the gain per year, we divide the total gain by the number of years:
\[ \text{Gain per year} = \frac{\text{Gain}}{2} = \frac{225}{2} = 112.5 \text{ Rs.} \]

### Final Answer
The gain in the transaction per year is **Rs. 112.5**.

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