Thirty eight percent of a certain number is equal to 133. Using this information, determine the value of the original number.

Introduction / Context:
This is another reverse percentage problem. Instead of finding a percentage of a known quantity, you are given the percentage result and asked to recover the original number. Questions like this are common in topics such as profit and loss, taxation, and data analysis.

Given Data / Assumptions:

• 38 percent of a number N equals 133.
• Formally, (38 / 100) * N = 133.
• Your goal is to solve for N.

Concept / Approach:
The general relation is p percent of N = V, which means (p / 100) * N = V. Rearranging gives N = (V * 100) / p. Here, p = 38 and V = 133. After substituting, we simplify the fraction to find the exact original number.

Step-by-Step Solution:
Step 1: Write the equation: (38 / 100) * N = 133. Step 2: Solve for N: N = (133 * 100) / 38. Step 3: Compute 133 * 100 = 13,300. Step 4: Divide 13,300 by 38. Since 38 * 350 = 13,300, we have N = 350.

Verification / Alternative check:
Check the answer by recalculating 38 percent of 350: (38 / 100) * 350 = 0.38 * 350 = 133. This matches the given value in the problem, so N = 350 is confirmed as correct.

Why Other Options Are Wrong:

• 340 gives 38 percent equal to 129.2, not 133.
• 360 gives 38 percent equal to 136.8, which is larger than 133.
• 355 gives 38 percent equal to 134.9, which does not match 133 exactly.

Common Pitfalls:
Learners sometimes mistakenly compute 38 percent of 133 instead of using 133 as the percentage result. Others may round the division incorrectly. Writing the algebraic equation clearly and checking with multiplication ensures accuracy.

Final Answer:
The original number is 350.