Question

25 percent of 25 percent of x is equal to 25. What is the value of x?

• A. 6.25
• B. 25
• C. 100
• D. 400
• E. 625

Hint:

Converting common percentages like 25%, 50%, and 75% to their simpler fractional equivalents (1/4, 1/2, 3/4) can make calculations significantly faster and less prone to error.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
This problem involves nested percentages. We need to translate the sentence into a single algebraic equation and solve for the unknown variable \(x\).
Step 2: Key Formula or Approach:
Translate the sentence into an equation. It's often easier to work with fractions or decimals instead of percentages.
25 percent = \( \frac{25}{100} = \frac{1}{4} \) or 0.25.
The equation becomes:
\[ \frac{1}{4} \times \left( \frac{1}{4} \times x \right) = 25 \] Step 3: Detailed Explanation:
Using the fractional form:
\[ \frac{1}{4} \times \frac{1}{4} \times x = 25 \] Multiply the fractions on the left side:
\[ \frac{1}{16} x = 25 \] To solve for \(x\), multiply both sides by 16:
\[ x = 25 \times 16 \] \[ x = 400 \] Alternatively, using decimals:
\[ 0.25 \times (0.25 \times x) = 25 \] \[ 0.0625 x = 25 \] \[ x = \frac{25}{0.0625} = \frac{25}{1/16} = 25 \times 16 = 400 \] Step 4: Final Answer:
The value of \(x\) is 400. This corresponds to option (D).