After two successive rises, the salary of Eckhrat Tolle, working in a BPO company became equal to `15/8` times of his initial salary. By how much percent was the salary was half of the rise in second time in percent?

Options

A. `82.5%`
B. `60%`
C. `50%`
D. Can't be determined

Answer

To solve the problem step by step, let's break it down:

### Step 1: Define the Initial Salary
Let the initial salary of Eckhrat Tolle be represented as \( S \). For simplicity, we can assume \( S = 8x \).

### Step 2: Determine the Final Salary
According to the problem, after two successive raises, the final salary becomes \( \frac{15}{8} \) times the initial salary. Therefore, we can express the final salary as:
\[ \text{Final Salary} = \frac{15}{8} \times S = \frac{15}{8} \times 8x = 15x \]

### Step 3: Understand Successive Increases
Let’s denote the first raise percentage as \( A \) and the second raise percentage as \( B \). The formula for successive increases is given by:
\[ \text{Final Salary} = S \left(1 + \frac{A}{100}\right) \left(1 + \frac{B}{100}\right) \]
Substituting the values we have:
\[ 15x = 8x \left(1 + \frac{A}{100}\right) \left(1 + \frac{B}{100}\right) \]

### Step 4: Simplify the Equation
Dividing both sides by \( 8x \):
\[ \frac{15}{8} = \left(1 + \frac{A}{100}\right) \left(1 + \frac{B}{100}\right) \]

### Step 5: Expand the Right Side
Expanding the right side gives:
\[ \frac{15}{8} = 1 + \frac{A}{100} + \frac{B}{100} + \frac{AB}{10000} \]

### Step 6: Rearranging the Equation
Rearranging the equation, we get:
\[ \frac{15}{8} - 1 = \frac{A}{100} + \frac{B}{100} + \frac{AB}{10000} \]
Calculating \( \frac{15}{8} - 1 \):
\[ \frac{15}{8} - \frac{8}{8} = \frac{7}{8} \]
So we have:
\[ \frac{7}{8} = \frac{A + B + \frac{AB}{100}}{100} \]

### Step 7: Multiply by 100
Multiplying through by 100 gives:
\[ 87.5 = A + B + \frac{AB}{100} \]

### Step 8: Analyze the Problem
At this point, we have one equation with two unknowns \( A \) and \( B \). Without additional information about either \( A \) or \( B \), we cannot determine their individual values. Therefore, we cannot find half of the rise in the second time in percent.

### Conclusion
Since we do not have enough information to determine the values of \( A \) and \( B \), we conclude that the answer is:
\[ \text{Cannot be determined} \]