Ramesh spends Rs. 38,460 on renovating his home and Rs. 24,468 on buying furniture. The remaining 28% of his total money is left as cash with him. What was the total amount of money Ramesh originally had?

Introduction / Context:
This is a reverse percentage problem involving spending and remaining money. Such questions are very common in aptitude tests under the percentage or profit and loss chapters. Instead of directly finding a percentage of a known total, we are given the spent amount and the percentage of the total that remains, and we have to work backwards to find the original total amount of money.

Given Data / Assumptions:

Amount spent on renovation = Rs. 38,460.
Amount spent on furniture = Rs. 24,468.
Remaining cash is 28% of the original total amount.
Total original amount is to be found.
We assume all values are in rupees and simple percentage arithmetic applies.

Concept / Approach:
Let the original total amount be T rupees. The total amount spent is the sum of the two given expenses. The remaining money is given as 28% of T, so the spent amount is the other 72% of T. Thus we can write:
spent amount = 72% of T = 0.72 * T Once we know the spent amount as a number, we can solve this simple linear equation to find T by dividing by 0.72.

Step-by-Step Solution:
Step 1: Compute the total amount spent. Total spent = 38,460 + 24,468 = 62,928. Step 2: Let the original total amount be T. Then 72% of T was spent. So, 0.72 * T = 62,928. Step 3: Solve for T by dividing both sides by 0.72. T = 62,928 / 0.72. Step 4: Perform the division: 62,928 / 0.72 = 87,400. Step 5: Therefore the original total amount Ramesh had was Rs. 87,400.

Verification / Alternative check:
To verify, compute 28% of 87,400 and check that the remaining plus the spent matches the total. First find 28% of 87,400: (28 / 100) * 87,400 = 24,472. Now add this remaining cash to the actual spent amount of 62,928. The sum is 62,928 + 24,472 = 87,400, which matches the original total, confirming that the calculation is consistent and correct.

Why Other Options Are Wrong:
Rs. 92,520 would give a spent portion of 72% equal to 66,614.4, not 62,928.
Rs. 88,470 would give 72% equal to 63,698.4, which is higher than the actual spent amount.
Rs. 90,150 would give 72% equal to 64,908, again not matching 62,928.
Rs. 80,000 would give 72% equal to 57,600, which is too low compared to the actual spent amount.

Common Pitfalls:
A typical error is to treat 28% as the spent portion rather than the remaining portion, which would lead to an incorrect equation. Another common mistake is to subtract 28% from the spent amount instead of linking it correctly to the original total. Some learners also forget to convert 72% into its decimal form 0.72, or they divide by 72 instead of 0.72. Careful reading of the phrase stating that 28% is the remaining amount is crucial for setting up the right equation.

Final Answer:
Ramesh originally had Rs. 87,400 in total.