If the monthly salary of an employee is increased by $2 \frac{2}{3}\%$, he gets ₹ 72 more. His monthly salary (in ₹) is

### Concept & Formula The percentage increase corresponds directly to the absolute increase in value. If a quantity $x$ increases by $R\%$, and the absolute increase is $V$, then $R\%$ of $x = V$. $$ \frac{R}{100} \times x = V $$ ### Step-by-Step Solution * **Given:** The increase in salary is $2 \frac{2}{3}\%$. The monetary value of this increase is ₹ 72. * Let the original monthly salary be $x$. * Convert the mixed fraction percentage into an improper fraction: $$ 2 \frac{2}{3}\% = \frac{3 \times 2 + 2}{3}\% = \frac{8}{3}\% $$ * Set up the equation based on the given condition: $$ \frac{8}{3}\% \text{ of } x = 72 $$ * Convert the percentage to a mathematical operation (divide by 100): $$ \left(\frac{8}{3 \times 100}\right) \times x = 72 $$ $$ \frac{8}{300} \times x = 72 $$ * Solve for $x$: $$ x = \frac{72 \times 300}{8} $$ $$ x = 9 \times 300 = 2700 $$ ### Exam Strategy & Shortcut Treat the percentage purely as a fraction. $\frac{8}{3}\% = \frac{8}{300} = \frac{2}{75}$. This means an increase of 2 parts on a base of 75 parts. We are given that $2 \text{ parts} = 72$. Therefore, $1 \text{ part} = 36$. The total salary (75 parts) $= 75 \times 36$. To multiply $75 \times 36$ quickly: $(100 - 25) \times 36 = 3600 - 900 = 2700$. ### Common Pitfall Students often forget to divide by 100 when dealing with fraction percentages, erroneously solving $\frac{8}{3} \times x = 72$, which leads to $x = 27$ (a clearly incorrect salary). Always remember the `%` symbol means $\times \frac{1}{100}$. ### Final Answer **Therefore, the correct answer is 2700.**