A Co-operative Bank gives H.B. loans under the condition that if the loan be cleared with interset in five years, the rate of simple interest per year is 5 % otherwise It will be 7 % Mr. Rahim and Mr. Ram take the same amount of H.B. loan and clear the loan with interest in 5 and 8 years respectively. If Ram pays Rs. 62,000 more, what is the amount of loan taken by each of them?

Options

A. Rs. 200000
B. Rs. 180000
C. Rs. 190000
D. Rs. 210000

Answer

To solve the problem step by step, we will first define the variables and then calculate the amounts paid by both Mr. Rahim and Mr. Ram based on the conditions provided.

### Step 1: Define the Loan Amount
Let the amount of loan taken by both Mr. Rahim and Mr. Ram be \( X \).

### Step 2: Calculate the Total Amount Paid by Mr. Rahim
Mr. Rahim pays off the loan in 5 years at a simple interest rate of 5%. The formula for the total amount paid with simple interest is:
\[ \text{Total Amount} = \text{Principal} + \text{Interest} \]
The interest for Mr. Rahim can be calculated as:
\[ \text{Interest} = \frac{X \times 5 \times 5}{100} = \frac{25X}{100} = \frac{X}{4} \]
Thus, the total amount paid by Mr. Rahim is:
\[ \text{Total Amount}_{\text{Rahim}} = X + \frac{X}{4} = \frac{4X}{4} + \frac{X}{4} = \frac{5X}{4} \]

### Step 3: Calculate the Total Amount Paid by Mr. Ram
Mr. Ram pays off the loan in 8 years at a simple interest rate of 7%. The interest for Mr. Ram can be calculated as:
\[ \text{Interest} = \frac{X \times 8 \times 7}{100} = \frac{56X}{100} = \frac{14X}{25} \]
Thus, the total amount paid by Mr. Ram is:
\[ \text{Total Amount}_{\text{Ram}} = X + \frac{14X}{25} = \frac{25X}{25} + \frac{14X}{25} = \frac{39X}{25} \]

### Step 4: Set Up the Equation Based on the Given Information
According to the problem, Mr. Ram pays Rs. 62,000 more than Mr. Rahim:
\[ \text{Total Amount}_{\text{Ram}} - \text{Total Amount}_{\text{Rahim}} = 62000 \]
Substituting the amounts we calculated:
\[ \frac{39X}{25} - \frac{5X}{4} = 62000 \]

### Step 5: Find a Common Denominator and Solve for \( X \)
The common denominator for 25 and 4 is 100. We will convert both fractions:
\[ \frac{39X}{25} = \frac{156X}{100}, \quad \frac{5X}{4} = \frac{125X}{100} \]
Now substituting back into the equation:
\[ \frac{156X}{100} - \frac{125X}{100} = 62000 \]
This simplifies to:
\[ \frac{31X}{100} = 62000 \]

### Step 6: Solve for \( X \)
Multiplying both sides by 100:
\[ 31X = 6200000 \]
Now, divide by 31:
\[ X = \frac{6200000}{31} = 200000 \]

### Conclusion
The amount of loan taken by each of them is Rs. 200,000.