The salaries of Ramesh, Ganesh and Rajesh were in the ratio $6:5:7$ in $2010$ , and in the ratio $3:4:3$ in $2015$ . If Ramesh's salary increased by $25\%$ during $2010-2015$ , then the percentage increase in Rajesh's salary during this period is closest to:

$9$

$7$

$8$

$10$

✅ Correct Option: 2

When we have ratios like $6:5:7$ , we can represent the actual salaries using a common multiplier.

In 2010: Let's say the salaries are $6x$ , $5x$ , and $7x$ respectively

Ramesh: $6x$

Ganesh: $5x$

Rajesh: $7x$

In 2015: Similarly, let's say the salaries are $3y$ , $4y$ , and $3y$ respectively

Ramesh: $3y$

Ganesh: $4y$

Rajesh: $3y$

The variables $x$ and $y$ represent the "unit value" for each time period. This lets us work with the ratios while keeping track of actual salary amounts.

We're told Ramesh's salary increased by 25% from 2010 to 2015.

Ramesh's salary in 2010: $6x$

Ramesh's salary in 2015: $3y$

Since there's a 25% increase: $3y = 6x \times 1.25 = 7.5x$

Therefore: $y = 2.5x$

By finding the relationship between $x$ and $y$ , we can now compare salaries across the two time periods.

Rajesh's salary in 2010: $7x$

Rajesh's salary in 2015: $3y = 3(2.5x) = 7.5x$

Percentage increase formula: $\tfrac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \times 100$

Rajesh's percentage increase:

$\tfrac{7.5x - 7x}{7x} \times 100 = \tfrac{0.5x}{7x} \times 100 = \tfrac{0.5}{7} \times 100$

$= \tfrac{1}{14} \times 100 = 7.14\%$

The percentage increase in Rajesh's salary is approximately 7%.

This method we use with ratio multipliers works for any ratio problem where we need to compare values across different time periods. We always look for the "bridge" information (like Ramesh's 25% increase here) to connect the two scenarios.

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