Sairam spent Rs. 38,460 on renovating his home and Rs. 24,468 on buying a TV set, after which he still had 28% of his total original amount left. What was the total amount of money he had initially?

Introduction / Context:
This question involves reverse percentage and basic algebra. Sairam spends fixed rupee amounts on renovation and on a TV, and is left with 28% of his original total. By treating the original amount as an unknown and expressing the remaining percentage in terms of that unknown, we can set up a simple linear equation and solve for his starting amount.

Given Data / Assumptions:

• Amount spent on renovation = Rs. 38,460.
• Amount spent on TV set = Rs. 24,468.
• He still has 28% of his original total amount left after both purchases.
• No other expenditures or incomes are involved.

Concept / Approach:
Let the original total amount be T. The total spent is the sum of the two given expenditures. The remaining money is 28% of T, that is 0.28 * T. We know that original total T equals the sum of money spent plus the remaining money. Hence we can write an equation T = (total spent) + 0.28 * T, and solve for T. This is a standard reverse percentage technique used in many aptitude questions.

Step-by-Step Solution:
Step 1: Let the original total amount be T. Step 2: Total amount spent = 38,460 + 24,468. Step 3: Compute total spent: 38,460 + 24,468 = 62,928. Step 4: Remaining money = 28% of T = 0.28 * T. Step 5: Original total T must equal money spent plus remaining money. So T = 62,928 + 0.28 * T. Step 6: Rearrange the equation: T - 0.28 * T = 62,928. Step 7: This gives 0.72 * T = 62,928. Step 8: Solve for T: T = 62,928 / 0.72. Step 9: 62,928 / 0.72 = 87,400. Step 10: Therefore, the original amount was Rs. 87,400.

Verification / Alternative check:
Check by working forward from Rs. 87,400. Sairam spends 38,460 and 24,468, which totals 62,928. Remaining amount = 87,400 - 62,928 = 24,472. Now check if this is 28% of 87,400: 28% of 87,400 = 0.28 * 87,400 = 24,472. This matches exactly, confirming that the original amount is correctly found as Rs. 87,400.

Why Other Options Are Wrong:
If the original amount were Rs. 68,700, 28% of that would not leave enough to cover the given expenditures. Similar mismatches occur for Rs. 74,000 and Rs. 94,060; when you compute 28% of those values and add the spent amount, the totals do not align with the required consistency condition that T equals spent plus remaining. Only Rs. 87,400 satisfies the equation exactly.

Common Pitfalls:
One frequent error is to treat 28% as the spent portion instead of the remaining portion. Another pitfall is failing to set up the equation correctly, for example writing T = 0.28 * T - spent instead of T = spent + 0.28 * T. Some students also mistakenly divide the spent amount by 0.28 instead of 0.72. Always remember: if 28% remains, then 72% has been spent, and the spent amount equals 0.72 * T, while the total is the sum of spent and remaining portions.

Final Answer:
Sairam originally had Rs. 87,400.