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The question in the image asks the following:

- A's salary is first increased by 25% and then decreased by 20%.
- B's salary is increased by 20% and then decreased by 25%.
- Find the ratio of the initial salary of B to that of the initial salary of A.

### Solution:
Let the initial salary of A be \( A_0 \) and the initial salary of B be \( B_0 \).

#### For A:
- First, A's salary is increased by 25%. This gives the new salary as:
  \[
  A_1 = A_0 \times (1 + 0.25) = A_0 \times 1.25
  \]
- Then, A's salary is decreased by 20%. The final salary after the decrease is:
  \[
  A_{\text{final}} = A_1 \times (1 - 0.20) = A_0 \times 1.25 \times 0.80 = A_0 \times 1.00
  \]
So, A's final salary is equal to \( A_0 \), meaning no net change to A's salary.

#### For B:
- First, B's salary is increased by 20%. This gives the new salary as:
  \[
  B_1 = B_0 \times (1 + 0.20) = B_0 \times 1.20
  \]
- Then, B's salary is decreased by 25%. The final salary after the decrease is:
  \[
  B_{\text{final}} = B_1 \times (1 - 0.25) = B_0 \times 1.20 \times 0.75 = B_0 \times 0.90
  \]
So, B's final salary is 90% of \( B_0 \).

#### Ratio of B's initial salary to A's initial salary:
From the question, we know that the final salary of A equals the final salary of B. Therefore:
\[
A_{\text{final}} = B_{\text{final}}
\]
Substitute the expressions for the final salaries:
\[
A_0 = B_0 \times 0.90
\]
Thus, the ratio of the initial salaries of B to A is:
\[
\frac{B_0}{A_0} = \frac{1}{0.90} = \frac{10}{9}
\]

### Final Answer: 
The ratio of the initial salaries of B to A is \( 10:9 \).

Would you like more details or have any questions?

### Related Questions:
1. What is the effect of multiple percentage changes on a salary?
2. How do you calculate the net change after successive percentage increases and decreases?
3. What is the general formula for calculating percentage changes?
4. How do you express percentage increases and decreases as fractions?
5. How do you find the ratio between two values after percentage changes?

### Tip:
When dealing with successive percentage changes, always apply them step by step to avoid errors, especially with decreases after increases.

A's salary is first increased by 25% and then decreased by 20%. The result is the same as B's salary increased by 20% and then reduced by 25%. Find the ratio of initial salaries of B to that of the initial salary of A.

This problem explores the effect of successive percentage increases and decreases on salaries and calculates the ratio of the initial salaries of two individuals. Learn how to handle percentage changes step-by-step. Suitable for students in Grades 10-12.

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