After deducting 12 percent from a certain sum and then deducting 25 percent from the remainder, Rs. 2,508 is left. What was the initial sum before any deductions were made?

Introduction / Context:
This question involves successive percentage deductions from an unknown original sum. It tests your understanding of how consecutive percentage changes combine and how to reverse them to recover the original amount from the final remaining value.

Given Data / Assumptions:

• Original sum = S (unknown).
• First deduction = 12 percent of S.
• Second deduction = 25 percent of the remaining amount after the first deduction.
• Final amount left after both deductions = Rs. 2,508.

Concept / Approach:
A deduction of 12 percent means 88 percent of the amount is left after the first step. A deduction of 25 percent from the remainder means only 75 percent of that remainder is left. Therefore, the final amount is S * 0.88 * 0.75. We equate this product to 2,508 and solve for S using basic algebra.

Step-by-Step Solution:
Step 1: After the first deduction of 12 percent, amount left = S * (100 − 12) / 100 = S * 0.88. Step 2: From this remainder, 25 percent is deducted, leaving 75 percent of it. Step 3: Amount left after second deduction = S * 0.88 * 0.75. Step 4: Compute 0.88 * 0.75 = 0.66. Step 5: So final amount = S * 0.66 = 2,508. Step 6: Solve for S: S = 2,508 / 0.66. Step 7: Compute 2,508 / 0.66 = 3,800.

Verification / Alternative check:
Check stepwise: starting from 3,800, first deduct 12 percent. Twelve percent of 3,800 is (12 / 100) * 3,800 = 456. Remainder = 3,800 − 456 = 3,344. Now deduct 25 percent of 3,344, which is (25 / 100) * 3,344 = 836. Final remainder = 3,344 − 836 = 2,508, exactly matching the given amount. This confirms S = 3,800 is correct.

Why Other Options Are Wrong:

• 3,500, 3,450, and 3,970, when processed through the same successive deductions, do not result in 2,508; their final values are different.

Common Pitfalls:
One common mistake is to add the percentages 12 percent and 25 percent and treat the total deduction as 37 percent once, which is incorrect because the second deduction is taken on a reduced base. Another error is reversing the operations incorrectly when solving for the original sum. Using the product of the remaining percentages (0.88 and 0.75) and then solving the simple equation is the cleanest method.

Final Answer:
The initial sum before any deductions were made is Rs. 3,800.