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 B's salary to the of A's.

Options

A. `9:10`
B. `10:9`
C. `9:12`
D. `12:9`

Answer

To solve the problem step by step, we will denote A's salary as \( A \) and B's salary as \( B \).

### Step 1: Calculate A's salary after the increase and decrease
A's salary is first increased by 25%.
- The new salary after the increase is:
\[ A' = A + 0.25A = A(1 + 0.25) = A \times \frac{125}{100} = \frac{125A}{100} \]

Next, A's salary is decreased by 20%.
- The new salary after the decrease is:
\[ A'' = A' - 0.20A' = A' \times (1 - 0.20) = A' \times \frac{80}{100} = \frac{125A}{100} \times \frac{80}{100} = \frac{125 \times 80A}{100 \times 100} = \frac{10000A}{10000} = \frac{10000A}{10000} = 100A \]

### Step 2: Calculate B's salary after the increase and decrease
B's salary is first increased by 20%.
- The new salary after the increase is:
\[ B' = B + 0.20B = B(1 + 0.20) = B \times \frac{120}{100} = \frac{120B}{100} \]

Next, B's salary is decreased by 25%.
- The new salary after the decrease is:
\[ B'' = B' - 0.25B' = B' \times (1 - 0.25) = B' \times \frac{75}{100} = \frac{120B}{100} \times \frac{75}{100} = \frac{120 \times 75B}{100 \times 100} = \frac{9000B}{10000} = 90B \]

### Step 3: Set the two results equal
According to the problem, the final amounts after the adjustments are equal:
\[ A'' = B'' \]
This gives us the equation:
\[ 100A = 90B \]

### Step 4: Solve for the ratio of B's salary to A's salary
Rearranging the equation to find the ratio \( \frac{B}{A} \):
\[ \frac{B}{A} = \frac{100A}{90B} = \frac{10}{9} \]

### Final Result
Thus, the ratio of B's salary to A's salary is:
\[ \frac{B}{A} = \frac{10}{9} \]