Gaurav spends 30% of his monthly income on food articles, 40% of the remaining on conveyance and clothes and saves 50% of the remaining. If his monthly salary is ₹ 18,400, how much money does he save every month?

### Concept & Formula For successive expenditures, you can find the final remaining amount (savings) directly by multiplying the original income by the remaining fractions at each step. $$\text{Final Value} = \text{Initial Value} \times \left(1 - \frac{R_1}{100}\right) \times \left(1 - \frac{R_2}{100}\right) \dots$$ ### Step-by-Step Solution * Let the initial monthly salary be ₹ 18,400. * Gaurav spends 30% on food. The remaining amount is $100\% - 30\% = 70\%$. * He spends 40% of the remaining on conveyance and clothes. The new remaining amount is $100\% - 40\% = 60\%$ of the previous remainder. * He saves 50% of the final remainder. * Chain the remaining percentages together to find the overall savings percentage: $$\text{Savings} = 18400 \times 70\% \times 60\% \times 50\%$$ * Convert percentages to decimals (or fractions) and calculate: $$\text{Savings} = 18400 \times 0.70 \times 0.60 \times 0.50$$ $$\text{Savings} = 18400 \times (0.70 \times 0.30)$$ $$\text{Savings} = 18400 \times 0.21$$ * Perform the final multiplication: $$18400 \times 0.21 = 184 \times 21 = 3864$$ ### Exam Strategy & Shortcut Use the fraction equivalent method to multiply quickly. Remaining after food = $\frac{7}{10}$. Remaining after conveyance = $\frac{6}{10} = \frac{3}{5}$. Savings portion = $\frac{1}{2}$. Total savings fraction = $\frac{7}{10} \times \frac{3}{5} \times \frac{1}{2} = \frac{21}{100}$. Now, just find 21% of 18400. $20\%$ of $18400 = 3680$. $1\%$ of $18400 = 184$. $3680 + 184 = 3864$. This avoids heavy long multiplication. ### Common Pitfall A common trap is adding the percentages together ($30\% + 40\% + 50\% = 120\%$) which is impossible, or subtracting them all from 100 base simultaneously. The keyword "remaining" dictates that each percentage applies only to the diminished balance, not the original salary. ### Final Answer **Therefore, the correct answer is ₹ 3864.**