A number increased by 137 1/2% has an increment of 33. What is the original number?

Introduction / Context:
This question assesses understanding of percentage increase where the increment (absolute change) is specified. Converting a mixed percentage to a decimal allows direct computation of the base value.

Given Data / Assumptions:

• Increase rate = 137 1/2% = 137.5% = 1.375 as a decimal.
• Increment amount (final − original) = 33.

Concept / Approach:
If a quantity N is increased by r%, the increment is (r/100) * N. Here, 33 corresponds to 137.5% of N. Solve N = 33 / 1.375. Mixed percentages should be converted carefully to decimals or fractions before solving.

Step-by-Step Solution:
r = 137.5% = 1.375Increment = r * N ⇒ 33 = 1.375 * NN = 33 / 1.375 = 24

Verification / Alternative check:
Check: 137.5% of 24 = 24 * 1.375 = 33. The increment matches the stated value, confirming N = 24.

Why Other Options Are Wrong:
25 and 27 are close but yield increments 34.375 and 37.125; 22 gives 30.25; 28 gives 38.5, none equal to 33.

Common Pitfalls:
Confusing the increment with the final value, or interpreting 137 1/2% as 1.37 instead of 1.375. Always convert the mixed percent correctly.

Final Answer:
24