The banker's discount on a certain sum due 4 yr, hence is - of the true discount. 10 Find the rate per cent per annum.

Options

A. `2.5%`
B. 0.05
C. `5.5%`
D. `1.5%`

Answer

To solve the problem, we need to find the rate per cent per annum given that the banker's discount (BD) on a certain sum due in 4 years is 10 times the true discount (TD).

### Step-by-Step Solution:

1. **Understand the Relationship**:
We know that the banker's discount (BD) is related to the true discount (TD) by the equation:
\[ BD = \frac{10}{1} \times TD \]
This means that the banker's discount is 10 times the true discount.

2. **Use the Formula for Banker's Discount**:
The formula for banker's discount is:
\[ BD = \frac{Time \times Rate}{100} \]
Here, the time is given as 4 years. Let \( R \) be the rate we need to find.

3. **Substitute the Values**:
Since we know that \( BD = 10 \times TD \) and \( TD \) can be expressed in terms of \( BD \) as:
\[ TD = \frac{BD}{10} \]
We can substitute \( BD \) in the formula:
\[ BD = \frac{4 \times R}{100} \]

4. **Set Up the Equation**:
Since \( BD = 10 \times TD \), we can write:
\[ BD = 10 \times \frac{BD}{10} \]
This simplifies to:
\[ BD = BD \]
We will now solve for \( R \) using the banker's discount formula:
\[ BD = \frac{4R}{100} \]

5. **Cross Multiply to Solve for R**:
Since we know \( BD = 10 \):
\[ 10 = \frac{4R}{100} \]
Cross multiplying gives:
\[ 1000 = 4R \]

6. **Calculate R**:
Now, divide both sides by 4:
\[ R = \frac{1000}{4} = 250 \]

7. **Final Rate Calculation**:
The rate per cent per annum is:
\[ R = 250\% \]

### Conclusion:
The rate per cent per annum is **250%**.