What must be the rate of interest in order that the discount on Rs. `774cdot76` payable at the end of 3 years may be Rs. `83cdot01`?

Options

A. `3%`
B. `2%`
C. `4%`
D. None of these

Answer

To find the rate of interest such that the discount on Rs. 774.76 payable at the end of 3 years is Rs. 83.01, we can use the formula for true discount:

\[ TD = \frac{P \times R \times T}{100 + R \times T} \]

Where:
- \( TD \) = True Discount
- \( P \) = Present Value (or Principal)
- \( R \) = Rate of interest
- \( T \) = Time in years

Given:
- \( TD = 83.01 \)
- \( P = 774.76 \)
- \( T = 3 \)

### Step 1: Substitute the known values into the formula
We start by substituting the known values into the formula:

\[ 83.01 = \frac{774.76 \times R \times 3}{100 + 3R} \]

### Step 2: Simplify the equation
Now, let's simplify the equation:

\[ 83.01(100 + 3R) = 774.76 \times R \times 3 \]

Expanding both sides:

\[ 8301 + 249.03R = 2324.28R \]

### Step 3: Rearranging the equation
Now, we will rearrange the equation to isolate \( R \):

\[ 8301 = 2324.28R - 249.03R \]

Combine like terms:

\[ 8301 = 2075.25R \]

### Step 4: Solve for \( R \)
Now, divide both sides by 2075.25 to find \( R \):

\[ R = \frac{8301}{2075.25} \]

Calculating the value:

\[ R \approx 4 \]

### Final Answer
Thus, the rate of interest \( R \) is approximately \( 4\% \).

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