Smita was supposed to multiply a number by 36 but instead multiplied it by 63 and got an answer that was 3834 more than the correct product. What was the number?

Introduction:
This error-analysis problem relies on the difference between two multipliers. If the wrong multiplier is higher, the result is greater by (wrong − correct) * number. Use the stated excess to back-calculate the number.

Given Data / Assumptions:

• Correct multiplier = 36; wrong multiplier = 63.
• Excess in result = 3834.
• Let the intended number be N.

Concept / Approach:
Excess = (63 − 36) * N = 27N. Hence N = excess / 27. Compute cleanly and compare with options.

Step-by-Step Solution:

Verification / Alternative check:
Correct product: 36 * 142 = 5112. Wrong product: 63 * 142 = 8946. Difference = 8946 − 5112 = 3834, as given.

Why Other Options Are Wrong:
Substituting 152, 126, 148, 114 into 27N does not yield 3834.

Common Pitfalls:
Using sum rather than difference of multipliers, or arithmetic slips in division.

Final Answer:
142