From the salary of an officer, 10% is deducted as house rent, 20% of the rest, he spends on conveyance, 20% of the rest he pays as income tax and 10% of the balance, he spends on clothes. Then, he is left with ₹ 15,552. Find his total salary.

### Concept & Formula This is a pure successive percentage problem marked by the repeating phrase "of the rest" or "of the balance". The final amount is the product of the original amount multiplied by the remaining fractions at each individual step. $$\text{Final Value} = \text{Initial} \times \left(1 - \frac{r_1}{100}\right) \times \left(1 - \frac{r_2}{100}\right) \times \left(1 - \frac{r_3}{100}\right) \dots$$ ### Step-by-Step Solution * Let the officer's total salary be $x$. * Track the remaining percentage after each specific deduction: * After $10\%$ rent, he has $90\%$ left ($0.9$). * After $20\%$ conveyance, he has $80\%$ of the rest left ($0.8$). * After $20\%$ tax, he has $80\%$ of the rest left ($0.8$). * After $10\%$ clothes, he has $90\%$ of the balance left ($0.9$). * Set up the unified equation equating to the final leftover amount (₹ 15,552): $$x \times 0.9 \times 0.8 \times 0.8 \times 0.9 = 15552$$ * Multiply the decimals: $$x \times (0.9 \times 0.9) \times (0.8 \times 0.8) = 15552$$ $$x \times (0.81) \times (0.64) = 15552$$ $$x \times 0.5184 = 15552$$ * Solve for $x$: $$x = \frac{15552}{0.5184} = \frac{155520000}{5184}$$ $$x = 30000$$ ### Exam Strategy & Shortcut Working with standard fractions is significantly faster and less prone to decimal errors than multiplying large numbers. $$0.9 = \frac{9}{10}$$ $$0.8 = \frac{4}{5}$$ Equation becomes: $$x \times \frac{9}{10} \times \frac{4}{5} \times \frac{4}{5} \times \frac{9}{10} = 15552$$ $$x \times \frac{1296}{2500} = 15552$$ Recognize that $1296 \times 12 = 15552$ (or divide it step-by-step by 9, then 4, etc.). $$x = 12 \times 2500 = 30000$$ ### Common Pitfall The primary mistake is ignoring the phrase "of the rest" and incorrectly summing up all deductions ($10\% + 20\% + 20\% + 10\% = 60\%$) and assuming he is left with $40\%$ of his total salary. ### Final Answer **Therefore, the correct answer is ₹ 30,000.**