Question

150% of what number is 120?

• A. 80
• B. 90
• C. 180
• D. 270
• E. 300

Hint:

Think of 150% as 1.5 or 3/2. The question becomes "3/2 times what number is 120?". To find the number, you can multiply 120 by the reciprocal of 3/2, which is 2/3. So, \(120 \times \frac{2}{3} = 40 \times 2 = 80\).

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This is a reverse percentage problem where we are given the result after applying a percentage and need to find the original number.
Step 2: Key Formula or Approach:
Let the unknown number be \(x\). The problem can be set up as an equation:
\[ \left( \frac{150}{100} \right) \times x = 120 \]
Step 3: Detailed Explanation:
Convert 150% into a decimal:
\[ 150% = \frac{150}{100} = 1.5 \]
Now, solve the equation for \(x\):
\[ 1.5 \times x = 120 \]
To isolate \(x\), divide both sides by 1.5:
\[ x = \frac{120}{1.5} \]
To make the division easier, multiply the numerator and denominator by 10:
\[ x = \frac{1200}{15} \]
\[ x = 80 \]
Step 4: Final Answer:
The original number is 80, which corresponds to option (A).