Vinay decided to donate 5% of his salary. On the day of donation he changed his mind and donated ₹ 1687.50, which was 75% of what he had decided earlier. How much is Vinay's salary?

### Concept & Logic The problem requires calculating the original base amount (salary) when a percentage of a percentage is given. The final donated amount is 75% of the 5% that was initially decided. $$ \text{Final Amount} = \text{Salary} \times 5\% \times 75\% $$ ### Step-by-Step Solution * **Given:** Initially decided donation = 5% of salary. Actual donation = ₹ 1687.50, which is 75% of the decided amount. * Let Vinay's total salary be $x$. * Amount decided to donate = $5\%$ of $x = 0.05x$. * Amount actually donated = $75\%$ of $0.05x$. * Set up the equation based on the actual donation: $$ 0.75 \times 0.05x = 1687.50 $$ * Simplify the percentages to fractions for easier calculation: $$ \left(\frac{75}{100}\right) \times \left(\frac{5}{100}\right) \times x = 1687.50 $$ $$ \left(\frac{3}{4}\right) \times \left(\frac{1}{20}\right) \times x = 1687.50 $$ $$ \frac{3}{80} \times x = 1687.50 $$ * Solve for $x$: $$ x = \frac{1687.50 \times 80}{3} $$ $$ x = 562.50 \times 80 = 45000 $$ ### Exam Strategy & Shortcut Use the fraction equivalent method to avoid messy decimals. $5\% = \frac{1}{20}$ and $75\% = \frac{3}{4}$. The effective donation is $\frac{1}{20} \times \frac{3}{4} = \frac{3}{80}$ of the salary. If $3$ units $= 1687.50$, then $1$ unit $= 562.50$. Total salary ($80$ units) $= 80 \times 562.50 = 45000$. ### Common Pitfall A frequent mistake is assuming the ₹ 1687.50 is 75% of the total salary, or calculating 75% of 5% by adding/subtracting them instead of multiplying. Always remember "of" implies multiplication. ### Final Answer **Therefore, the correct answer is ₹ 45000.**