Calculating New Salary Ratio After Percentage Increase

This problem involves calculating the new ratio of salaries after each salary is increased by a certain percentage. We are given the initial ratio of the salaries of three people and the respective percentage increases.

Understanding the Initial Salary Ratio

The initial salaries of Ravi, Anil, and Kavita are in the ratio 1 : 3 : 6.

Let's assume a common multiplier for the ratio. Let the initial salaries be:

• Ravi's initial salary: $1 \times x = x$
• Anil's initial salary: $3 \times x = 3x$
• Kavita's initial salary: $6 \times x = 6x$

where $x$ is a common factor.

Calculating the Increased Salaries

Now, the salaries are increased by different percentages:

• Ravi's salary is increased by 5%.
• Anil's salary is increased by 10%.
• Kavita's salary is increased by 15%.

To find the new salary, we add the percentage increase to the original salary. An increase of $P\%$ means the new value is the original value plus $P\%$ of the original value, which is original value $\times (1 + P/100)$.

Let's calculate the new salary for each person:

• Ravi's new salary: Initial salary $\times (1 + 5/100) = x \times (1 + 0.05) = x \times 1.05 = 1.05x$
• Anil's new salary: Initial salary $\times (1 + 10/100) = 3x \times (1 + 0.10) = 3x \times 1.10 = 3.30x$
• Kavita's new salary: Initial salary $\times (1 + 15/100) = 6x \times (1 + 0.15) = 6x \times 1.15 = 6.90x$

Forming the New Ratio of Salaries

The new ratio of the salaries of Ravi, Anil, and Kavita is the ratio of their new salaries:

New Ratio = Ravi's new salary : Anil's new salary : Kavita's new salary

New Ratio = $1.05x : 3.30x : 6.90x$

Simplifying the New Salary Ratio

To simplify the ratio, we can cancel out the common factor $x$.

Ratio = $1.05 : 3.30 : 6.90$

To work with whole numbers, we can multiply all parts of the ratio by 100 to remove the decimals:

Ratio = $1.05 \times 100 : 3.30 \times 100 : 6.90 \times 100$

Ratio = $105 : 330 : 690$

Now, we need to simplify this ratio by dividing all numbers by their greatest common divisor (GCD).

All numbers end in 0 or 5, so they are divisible by 5.

• $105 \div 5 = 21$
• $330 \div 5 = 66$
• $690 \div 5 = 138$

The ratio becomes $21 : 66 : 138$.

Now, check if these numbers have common factors. $21 = 3 \times 7$, $66 = 2 \times 3 \times 11$, $138 = 2 \times 3 \times 23$. The common factor is 3.

Divide all parts by 3:

• $21 \div 3 = 7$
• $66 \div 3 = 22$
• $138 \div 3 = 46$

The simplified ratio is $7 : 22 : 46$.

This is the new ratio of their salaries after the given percentage increases.

The new salaries are in the ratio $1.05x : 3.30x : 6.90x$. Simplifying this ratio gives $7 : 22 : 46$.

Revision Table: Ratio and Percentage Increase

Additional Information: Solving Ratio and Percentage Questions

When tackling problems involving ratios and percentages, it's often helpful to represent the initial quantities using a common variable, like $x$. This allows you to set up expressions for the new quantities after percentage changes are applied.

Remember that a percentage increase of $P\%$ can be calculated by multiplying the original amount by $(1 + P/100)$. For example, a 10% increase is multiplication by $1 + 10/100 = 1.10$. A 5% increase is multiplication by $1 + 5/100 = 1.05$. A 15% increase is multiplication by $1 + 15/100 = 1.15$.

After finding the new quantities, form the ratio and simplify it by dividing all parts by any common factors. Simplifying ratios is similar to simplifying fractions.

These types of ratio and percentage problems are common in quantitative aptitude tests and help assess your understanding of basic arithmetic and proportional reasoning.