A number is decreased to 72 1/2% (i.e., to 0.725 of itself) and the result is 87. Find the original number.

Introduction / Context:
This is the mirror of “increase to” problems. “Decreased to 72 1/2%” means the final equals 72.5% of the original. We reverse the percent change to recover the initial value.

Given Data / Assumptions:

• Final value = 87.
• Final = 72 1/2% of original = 0.725 of original.
• 0.725 = 29/40 for exact calculation.

Concept / Approach:
If original is x, then 0.725x = 87 ⇒ x = 87 / 0.725. Using fractions avoids rounding: x = 87 / (29/40) = 87 * 40 / 29.

Step-by-Step Solution:

Verification / Alternative check:
Check: 120 reduced to 72.5% ⇒ 120 * 0.725 = 87. Correct.

Why Other Options Are Wrong:
110, 135, 58 are results of using 27/40 or 3/4 mistakenly, or of subtracting percentages incorrectly.

Common Pitfalls:
Interpreting “decreased by 72 1/2%.” The phrase here is “decreased to,” which means multiply by 0.725, not subtract 72.5 points.

Final Answer:
120