Salary Ratio Calculation Steps
This problem involves calculating the new ratio between two salaries after applying percentage increases.
Initial Salary Ratio
Let the initial salaries of A and B be $4x$ and $5x$ respectively, based on the given ratio of 4:5.
Calculating New Salaries
A's salary is increased by 10%:
- Increase amount = $10\% \times 4x = 0.10 \times 4x = 0.4x$
- A's new salary = $4x + 0.4x = 4.4x$
B's salary is increased by 20%:
- Increase amount = $20\% \times 5x = 0.20 \times 5x = 1.0x$
- B's new salary = $5x + 1.0x = 6.0x$
Determining the New Ratio
The new ratio of A's salary to B's salary is calculated by dividing their new salaries:
- New Ratio = $\frac{\text{A's new salary}}{\text{B's new salary}} = \frac{4.4x}{6.0x}$
- Simplify the ratio: $\frac{4.4}{6.0} = \frac{44}{60}$
- Further simplify by dividing both numbers by their greatest common divisor (4): $\frac{44 \div 4}{60 \div 4} = \frac{11}{15}$
Therefore, the new ratio of A's salary to B's salary is 11:15.
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