Thirty-six percent of what number is equal to 18?

Introduction / Context:
This is another reverse percentage question. Instead of asking for 36% of a known number, the question gives the result of the percentage calculation (18) and asks us to find the original number. This type of question commonly appears in aptitude tests and is important for understanding how to work backwards with percentages.

Given Data / Assumptions:

Percentage involved = 36%.
36% of an unknown number is equal to 18.
We need to find the unknown original number.
All calculations use simple percentage arithmetic with no additional conditions.

Concept / Approach:
Let the unknown number be N. The statement 36% of N is 18 can be written as:
0.36 * N = 18 To find N, we can divide 18 by 0.36. This is the standard method of reversing a percentage calculation: divide the result by the decimal form of the percentage.

Step-by-Step Solution:
Step 1: Let the unknown number be N. Step 2: According to the question, 36% of N = 18. Step 3: Convert 36% to decimal: 36% = 36 / 100 = 0.36. Step 4: Set up the equation: 0.36 * N = 18. Step 5: Divide both sides of the equation by 0.36. N = 18 / 0.36. Step 6: Compute 18 / 0.36. Since 0.36 = 36 / 100, we have N = 18 * (100 / 36) = (18 * 100) / 36. Step 7: Simplify (18 * 100) / 36 = 1800 / 36 = 50. Step 8: Therefore, the required original number is 50.

Verification / Alternative check:
To confirm, calculate 36% of 50 and see if the result is 18. Compute (36 / 100) * 50 = 0.36 * 50. Multiplying 0.36 by 50 gives 18. Since this matches the given value, our solution is verified as correct.

Why Other Options Are Wrong:
If the number were 38, then 36% of 38 is 13.68, not 18.
If the number were 42, then 36% of 42 is 15.12, still not 18.
If the number were 62, then 36% of 62 is 22.32, which is greater than 18.
If the number were 54, then 36% of 54 is 19.44, again not equal to 18.

Common Pitfalls:
A frequent error is to multiply 18 by 0.36 instead of dividing by 0.36. Another typical mistake is to divide by 36 rather than 0.36, forgetting that the percentage should be converted into decimal form. Some learners also misread the question and compute 36% of 18 directly, which gives a much smaller number. Always identify whether you are moving from whole to part or from part back to whole.

Final Answer:
The number for which 36% equals 18 is 50.