Question

If ( 45% ) of a number is 180, then the number is:

• A. 360
• B. 400
• C. 420
• D. 450

Hint:

Use unitary breakdown to solve this mentally! If $45% = 180$, then dividing both sides by 9 gives $5% = 20$. Now, simply multiply by 20 to scale it up to the full amount: $5% \times 20 = 100%$, so $20 \times 20 = 400$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A percentage calculation defines a fractional part of an unknown whole value relative to 100. If a specific percentage share of a value is given, we can establish an algebraic equation to find the original full value ($100%$).

Step 2: Key Formula or Approach:
Let the unknown number be represented as $x$. $$\frac{\text{Percentage}}{100} \times x = \text{Given Value}$$

Step 3: Detailed Explanation:
According to the problem statement: \[ 45% \text{ of } x = 180 \] Convert the percentage into its equivalent fractional format: \[ \frac{45}{100} \times x = 180 \] Isolate the variable $x$ by multiplying both sides by $\frac{100}{45}$: \[ x = \frac{180 \times 100}{45} \] We know that $45 \times 2 = 90$, which means $45 \times 4 = 180$. Simplifying the division gives: \[ x = 4 \times 100 = 400 \]

Step 4: Final Answer:
The required number is 400.