A person borrowed 500 at 3% per annum S.I. and 600 at `4(1)/(2)%` per annum on the agreement that the whole sum, will be returned only when the total interest becomes 126. The number of years, after which the borrowed sum is to be returned, is :

Options

A. 2
B. 3
C. 4
D. 5

Answer

To solve the problem step by step, we will calculate the simple interest for both amounts borrowed and find out how many years it will take for the total interest to reach Rs 126.

### Step 1: Define the variables
Let the number of years be \( x \).

### Step 2: Calculate the simple interest for the first amount
The first amount borrowed is Rs 500 at an interest rate of 3% per annum. The formula for simple interest is:

\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]

Where:
- \( P \) = Principal amount (Rs 500)
- \( R \) = Rate of interest (3%)
- \( T \) = Time in years (x)

So, the simple interest for the first amount is:

\[ \text{SI}_1 = \frac{500 \times 3 \times x}{100} = 15x \]

### Step 3: Calculate the simple interest for the second amount
The second amount borrowed is Rs 600 at an interest rate of \( 4\frac{1}{2}\% \) per annum, which can be converted to a fraction as \( 4.5\% \) or \( \frac{9}{2}\% \).

Using the same formula for simple interest:

\[ \text{SI}_2 = \frac{600 \times \frac{9}{2} \times x}{100} = \frac{600 \times 9 \times x}{200} = 27x \]

### Step 4: Calculate the total interest
Now, we add the simple interests from both amounts:

\[ \text{Total Interest} = \text{SI}_1 + \text{SI}_2 = 15x + 27x = 42x \]

### Step 5: Set up the equation
According to the problem, the total interest becomes Rs 126. Therefore, we can set up the equation:

\[ 42x = 126 \]

### Step 6: Solve for \( x \)
To find \( x \), divide both sides of the equation by 42:

\[ x = \frac{126}{42} = 3 \]

### Conclusion
The number of years after which the borrowed sum is to be returned is \( 3 \) years.

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