Gaurav spends 30% of his monthly income on food items. He then spends 40% of the remaining amount on conveyance and clothes, and finally saves 50% of what is left. If his monthly salary is Rs. 18,400, how much money does he save every month?

Introduction / Context:
This problem is a practical example of successive percentage deductions and savings from a monthly income. Gaurav spends certain percentages of his income on different categories, with each percentage applied to the amount remaining after previous expenses. Finally, he saves a fixed percentage of the remaining money. The question asks for the exact amount he saves per month. This type of question strengthens skills in sequential percentage calculations and basic arithmetic operations.

Given Data / Assumptions:
- Monthly salary of Gaurav = Rs. 18,400.- He spends 30% of his salary on food.- He then spends 40% of the remaining amount on conveyance and clothes.- He saves 50% of the amount left after these two expenses.- We need to find the amount saved every month.

Concept / Approach:
The approach is to apply the spending percentages in the correct sequence, always computing each new percentage on the current remaining balance. First we deduct 30% of the salary, then 40% of the remainder, and then take 50% of what is left as savings. We must carefully track the remaining amount after each step to avoid mistakes. This is another example of how percentages operate on changing bases, not always on the original amount.

Step-by-Step Solution:
Step 1: Monthly salary = Rs. 18,400.Step 2: Spending on food = 30% of 18,400.Step 3: 30% of 18,400 = (30 / 100) * 18,400 = 0.30 * 18,400 = 5,520.Step 4: Remaining amount after food = 18,400 - 5,520 = 12,880.Step 5: Spending on conveyance and clothes = 40% of the remaining 12,880.Step 6: 40% of 12,880 = (40 / 100) * 12,880 = 0.40 * 12,880 = 5,152.Step 7: Remaining amount after conveyance and clothes = 12,880 - 5,152 = 7,728.Step 8: Savings = 50% of the remaining 7,728.Step 9: 50% of 7,728 = (50 / 100) * 7,728 = 0.50 * 7,728 = 3,864.Step 10: Therefore, Gaurav saves Rs. 3,864 every month.

Verification / Alternative check:
We can verify by computing what percentage of the original salary this saving represents.Savings as a fraction of salary = 3,864 / 18,400.Compute: 3,864 / 18,400 ≈ 0.21, or about 21% of the salary.This is reasonable, since he first spends 30%, then 40% of the remaining 70%, and then saves half of what is left. The sequence of deductions naturally leaves a moderate fraction of the original income as savings.

Why Other Options Are Wrong:
- 4903: This is higher than half of the amount remaining after all expenses and does not correspond to any correct step.- 5849: This would imply Gaurav is saving almost one-third of his salary, which conflicts with the high expenditure percentages.- 6789: Even larger and clearly incompatible with the sequence of 30% and then 40% expenses.

Common Pitfalls:
- Applying 40% directly to the original income instead of to the remaining amount after food expenses.- Applying 50% of the original income as savings instead of 50% of the amount left after both expenses.- Arithmetic mistakes in subtraction or percentage multiplication, especially with numbers like 12,880 and 7,728.- Confusing the order of operations, which changes the result significantly.

Final Answer:
Gaurav saves Rs. 3,864 every month.