Reverse percentage to find the base number: If 35% of a number is equal to 112, what is the original number?

Introduction / Context:This reverse-percentage question asks you to determine the base quantity when a known percentage of it is given. Such problems are frequently used in finance, discounting, and statistics for back-calculations from partial information.

Given Data / Assumptions:

• 35% of an unknown number N equals 112.
• We assume standard percentage definition: p% of N = (p/100) * N.

Concept / Approach:Translate the statement into an equation: 0.35 * N = 112. Solve for N by dividing 112 by 0.35. Always ensure the division is done precisely, because common decimal errors can lead to wrong options being selected.

Step-by-Step Solution:

Verification / Alternative check:Check by forward computation: 35% of 320 is 0.35 * 320 = 112, which matches the given condition exactly.

Why Other Options Are Wrong:300 yields 0.35 * 300 = 105 (too low). 380 gives 133 (too high). 35 is just the percentage, not the number. 280 gives 98 (too low). Only 320 satisfies the equation exactly.

Common Pitfalls:Accidentally computing 320 * 0.53 or mixing 35 and 0.35. Always convert percentages to decimal multipliers correctly: 35% → 0.35.

Final Answer:320