Initial Salary Ratio Explained

We are given that the initial ratio of the salaries of two employees is 3:4. Let's represent their salaries using a common multiplier, say '$x$'. So, the first employee's salary can be represented as $3x$ and the second employee's salary as $4x$.

Calculating Salary Percentage Increases

The problem states that the first employee's salary is increased by 10% and the second employee's salary is increased by 20%. Let's calculate the new salaries:

• First Employee's New Salary:

  The increase amount is 10% of $3x$, which is calculated as $0.10 \times 3x = 0.3x$. The new salary is the original salary plus the increase: $3x + 0.3x = 3.3x$. Alternatively, we can calculate it as $3x \times (1 + 0.10) = 3x \times 1.10 = 3.3x$.

• Second Employee's New Salary:

  The increase amount is 20% of $4x$, which is calculated as $0.20 \times 4x = 0.8x$. The new salary is the original salary plus the increase: $4x + 0.8x = 4.8x$. Alternatively, we can calculate it as $4x \times (1 + 0.20) = 4x \times 1.20 = 4.8x$.

Determining the New Salary Ratio

Now, we need to find the ratio of their new salaries. The new salaries are $3.3x$ and $4.8x$. The ratio is:

New Ratio = First Employee's New Salary : Second Employee's New Salary

New Ratio = $3.3x : 4.8x$

We can simplify this ratio by dividing both parts by '$x$':

New Ratio = $3.3 : 4.8$

Simplifying the Final Ratio

To express the ratio using whole numbers, we can multiply both parts by 10 to eliminate the decimals:

New Ratio = $(3.3 \times 10) : (4.8 \times 10)$

New Ratio = $33 : 48$

Finally, we simplify this ratio by finding the greatest common divisor (GCD) of 33 and 48. Both numbers are divisible by 3.

• $33 \div 3 = 11$
• $48 \div 3 = 16$

So, the simplified new ratio of their salaries is 11:16.