A number is increased to 137 1/2% (i.e., to 1.375 times itself) and the result is 33. What is the original number?

Introduction / Context: Problems involving a number being changed to a certain percent are straightforward reverse-percentage tasks. “Increased to 137 1/2%” means the final value equals 137.5% of the original, not that 137.5% was added.

Given Data / Assumptions:

• Final value = 33.
• Final value equals 137 1/2% of original.
• 137 1/2% = 137.5% = 11/8 as a multiplier.

Concept / Approach: Convert the mixed percent to a multiplier. If original is x, then (11/8)*x = 33. Solve for x by dividing 33 by 11/8 (equivalently multiplying by 8/11).

Step-by-Step Solution:

Verification / Alternative check: Increase 24 to 137.5%: 24 * 1.375 = 33. Correct.

Why Other Options Are Wrong: 22, 25, and 27 do not yield 33 when multiplied by 1.375; they result from misinterpreting “increase to” as “increase by.”

Common Pitfalls: Treating “to 137 1/2%” as adding 137.5% to the original (which would mean 237.5%). Always translate to a multiplier.

Final Answer: 24