Salary Comparison Setup

Let the initial salary of B be represented by $S_B$. Since A's salary is 40% more than B's, A's initial salary ($S_A$) can be expressed as:

$S_A = S_B + 0.40 \times S_B = 1.40 S_B$

Calculating New Salaries

B's salary increases by 20%. The new salary for B ($S_B'$) is:

$S_B' = S_B + 0.20 \times S_B = 1.20 S_B$

A's salary increases by x%. The new salary for A ($S_A'$) is:

$S_A' = S_A + \frac{x}{100} \times S_A = S_A \left(1 + \frac{x}{100}\right)$

Substituting $S_A = 1.40 S_B$:

$S_A' = 1.40 S_B \left(1 + \frac{x}{100}\right)$

Final Salary Condition

A's new salary ($S_A'$) is 25% more than B's new salary ($S_B'$). This means:

$S_A' = S_B' + 0.25 \times S_B' = 1.25 S_B'$

Solving for x

Now, substitute the expressions for $S_A'$ and $S_B'$ into the final condition:

$1.40 S_B \left(1 + \frac{x}{100}\right) = 1.25 (1.20 S_B)$

Cancel $S_B$ from both sides:

$1.40 \left(1 + \frac{x}{100}\right) = 1.25 \times 1.20$

$1.40 \left(1 + \frac{x}{100}\right) = 1.50$

Isolate the term with x:

$1 + \frac{x}{100} = \frac{1.50}{1.40}$

$1 + \frac{x}{100} = \frac{15}{14}$

Solve for $\frac{x}{100}$:

$\frac{x}{100} = \frac{15}{14} - 1$

$\frac{x}{100} = \frac{15 - 14}{14}$

$\frac{x}{100} = \frac{1}{14}$

Solve for x:

$x = \frac{1}{14} \times 100$

$x = \frac{100}{14} = \frac{50}{7}$

Converting to a decimal:

$x \approx 7.14\%$