Salary Calculation Based on Percentage Spending

This problem involves calculating a person's total monthly salary based on how they spend portions of it and their final savings. We need to work backward from the savings or set up an equation to find the initial salary.

Step-by-Step Solution

Let the person's total monthly salary be represented by '$S$'.

1. Calculate Spending on Food Items

• The person spends 40% of their salary on food.
• Amount spent on food = 40% of $S = 0.40 \times S = 0.40S$.

2. Calculate Remaining Salary After Food Expenses

• Salary remaining after food = Total Salary - Amount spent on food
• Remaining salary = $S - 0.40S = (1 - 0.40)S = 0.60S$.

3. Calculate Spending on Transport

• The person spends 50% of the *remaining* salary on transport.
• Amount spent on transport = 50% of $0.60S = 0.50 \times (0.60S) = 0.30S$.

4. Calculate Remaining Salary After Transport Expenses

• Salary remaining after transport = Salary after food - Amount spent on transport
• Remaining salary = $0.60S - 0.30S = (0.60 - 0.30)S = 0.30S$.

5. Calculate Spending on Clothes

• The person spends 30% of the *remaining* salary on clothes.
• Amount spent on clothes = 30% of $0.30S = 0.30 \times (0.30S) = 0.09S$.

6. Calculate Final Savings

• The final savings are the amount left after spending on food, transport, and clothes.
• Savings = Salary remaining after transport - Amount spent on clothes
• Savings = $0.30S - 0.09S = (0.30 - 0.09)S = 0.21S$.

7. Determine the Monthly Salary

• We are given that the person saves ₹1,260 every month.
• Therefore, we can set up the equation: $0.21S = 1260$.
• To find the total salary $S$, divide the savings by the percentage saved (expressed as a decimal):
• $S = \frac{1260}{0.21}$
• $S = \frac{126000}{21}$
• $S = 6000$.

Conclusion

The person's monthly salary is ₹6,000.

Verification

Let's check if spending ₹6,000 leads to savings of ₹1,260:

• Salary = ₹6,000
• Food (40%) = $0.40 \times 6000 = ₹2,400$
• Remaining = $6000 - 2400 = ₹3,600$
• Transport (50% of remaining) = $0.50 \times 3600 = ₹1,800$
• Remaining = $3600 - 1800 = ₹1,800$
• Clothes (30% of remaining) = $0.30 \times 1800 = ₹540$
• Final Savings = $1800 - 540 = ₹1,260$.

The calculated savings match the given amount, confirming the salary is correct.