After deducting 60% from a number and then 15% from the remainder, 1428 is left. What was the original number?

Introduction / Context:
This question tests the concept of successive percentage deductions from an original quantity. Such problems are common in aptitude exams and real life when a value is reduced in more than one step, for example through successive taxes, discounts, or losses. The key idea is that each percentage is applied on the remaining amount, not on the original number, and therefore we must treat them as multiplicative factors. Here, we know the final remaining value after two reductions and we are asked to recover the original number.

Given Data / Assumptions:
The original number is unknown and we can call it N.
First deduction is 60 percent of N, so only 40 percent of N remains.
Second deduction is 15 percent of the remaining amount, so 85 percent of that remainder is left.
After both deductions, the final amount is 1428.

Concept / Approach:
When a quantity is successively reduced by some percentages, we multiply the original quantity by the remaining percentage factors written in decimal form. Here the remaining fraction after a 60 percent deduction is 40 percent, which is 0.40. After that, a further 15 percent deduction leaves 85 percent, which is 0.85. Thus the final amount can be written as N * 0.40 * 0.85. We then set this expression equal to the given final value, 1428, and solve for N using simple algebra and division.

Step-by-Step Solution:
Let the original number be N. After deducting 60 percent, the remaining amount is 40 percent of N, which is 0.40 * N. Next, 15 percent is deducted from this remainder, so 85 percent is left: remaining amount = 0.85 * (0.40 * N). Therefore final amount = 0.40 * 0.85 * N = 0.34 * N. We are told the final amount is 1428, so 0.34 * N = 1428. Hence N = 1428 / 0.34. Compute N: 1428 / 0.34 = 4200. Therefore the original number is 4200.

Verification / Alternative check:
We can verify the answer by working forward from 4200. First deduction: 60 percent of 4200 is 0.60 * 4200 = 2520. Remaining amount is 4200 - 2520 = 1680, which matches 40 percent of 4200. Second deduction: 15 percent of 1680 is 0.15 * 1680 = 252. Remaining amount is 1680 - 252 = 1428. This final value matches the number given in the question, confirming that 4200 is correct. The arithmetic is consistent at each step, so no contradiction appears.

Why Other Options Are Wrong:
Option 3962 is wrong because 0.34 * 3962 is not equal to 1428; it gives a different final value. Option 4150 is also incorrect because applying 60 percent then 15 percent to 4150 does not produce 1428. Option 4300 is too large; 0.34 * 4300 gives a final amount greater than 1428. Only 4200 exactly reproduces the final value when both reductions are applied correctly.

Common Pitfalls:
A common mistake is to simply add 60 percent and 15 percent and assume a single 75 percent deduction, which is incorrect because the second percentage is applied after the first deduction. Another frequent error is to take 60 percent and 15 percent of the same original number rather than using the remainder. Some candidates also incorrectly round intermediate values, which can change the final result. Always convert percentages to decimal factors and apply them successively to avoid these issues.

Final Answer:
The original number before both deductions were applied was 4200.