An individual deposits 20% of 25% of 30% of the money he has into his bank account. If the deposited amount is Rs. 750, how much money did he initially have before depositing?

Introduction / Context:
This question deals with successive percentages applied to an initial amount, but in the form of a nested expression: 20% of 25% of 30% of the original amount. We are given the final deposited amount and asked to determine the original amount. This is a reverse percentage problem where we work backwards from a compound fraction of an unknown total.

Given Data / Assumptions:

• Let the original amount of money be X.
• The individual takes 30% of X.
• From that, he takes 25%.
• From that, he takes 20% and deposits it into the bank.
• The amount deposited = Rs. 750.
• We must find the value of X.

Concept / Approach:
We interpret “20% of 25% of 30% of X” as a chain of multiplications with decimal or fractional forms of the percentages. Specifically, 30% of X is 0.30 * X, 25% of that is 0.25 * 0.30 * X, and 20% of that is 0.20 * 0.25 * 0.30 * X. This final expression equals 750. We simplify the combined factor 0.20 * 0.25 * 0.30, set up an equation and solve for X by dividing 750 by the combined fraction.

Step-by-Step Solution:
Step 1: Let the original amount be X. Step 2: Compute the combined percentage factor. 30% of X = 0.30 * X. 25% of that amount = 0.25 * (0.30 * X) = 0.25 * 0.30 * X. 20% of that result = 0.20 * (0.25 * 0.30 * X) = 0.20 * 0.25 * 0.30 * X. Step 3: Multiply the decimal factors: 0.20 * 0.25 = 0.05. Step 4: Then 0.05 * 0.30 = 0.015. Step 5: Hence, deposited amount = 0.015 * X. Step 6: The deposited amount is given as Rs. 750. So 0.015 * X = 750. Step 7: Solve for X: X = 750 / 0.015. Step 8: 750 / 0.015 = 750 * (1 / 0.015) = 750 * (1000 / 15) = (750000 / 15) = 50,000. Step 9: Therefore, the individual initially had Rs. 50,000.

Verification / Alternative check:
Check by moving forward from Rs. 50,000. First, 30% of 50,000 is 0.30 * 50,000 = 15,000. Next, 25% of 15,000 is 0.25 * 15,000 = 3750. Finally, 20% of 3750 is 0.20 * 3750 = 750. This agrees exactly with the given deposited amount. Hence, the calculated original amount of Rs. 50,000 is correct.

Why Other Options Are Wrong:
If the original amount were Rs. 38,000, 20% of 25% of 30% of that would be 0.015 * 38,000 = 570, not 750. Similarly, for Rs. 47,000 we get 0.015 * 47,000 = 705, and for Rs. 35,000 we get 0.015 * 35,000 = 525. None of these match the required deposit of 750. Only Rs. 50,000 yields the correct deposit amount.

Common Pitfalls:
One mistake is to add the percentages (20 + 25 + 30) and treat the total 75% as a single direct percentage of X, which is incorrect. Another common error is to misplace the decimal when multiplying percentages, for example using 0.2 instead of 0.20 * 0.25 * 0.30. Always convert each percentage properly, multiply them stepwise, and remember that chaining percentages multiplies their fractions, it does not add them.

Final Answer:
The individual initially had Rs. 50,000.