The true discount on a certain sum of money due 4 yr hence is X 75 and the simple interest on the same sum for the same time and at the same rate of interest is X 225. Find the rate per cent.

Options

A. 0.25
B. 0.5
C. 0.31
D. 0.45

Answer

To solve the problem step by step, we will use the relationship between true discount, simple interest, and the rate of interest.

### Step 1: Understand the given values
- True Discount (TD) = ₹75
- Simple Interest (SI) = ₹225
- Time (T) = 4 years

### Step 2: Use the formula relating SI, TD, and the rate of interest (R)
The formula we will use is:
\[ \text{SI} - \text{TD} = \text{TD} \times R \times T \]

### Step 3: Substitute the known values into the formula
Substituting the values we have:
\[ 225 - 75 = 75 \times R \times 4 \]

### Step 4: Simplify the equation
First, calculate the left side:
\[ 225 - 75 = 150 \]
So, we have:
\[ 150 = 75 \times R \times 4 \]

### Step 5: Solve for R
Now, simplify the right side:
\[ 150 = 300R \]
To find R, divide both sides by 300:
\[ R = \frac{150}{300} = \frac{1}{2} \]

### Step 6: Convert R to percentage
To convert R into percentage, multiply by 100:
\[ R = \frac{1}{2} \times 100 = 50\% \]

### Conclusion
The rate of interest is **50%**.

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