Question

Which of the following multipliers will increase a given number by 25.3 % ?

• A. 12.53
• B. 1.253
• C. 13.53
• D. 125.3

Hint:

To quickly find the multiplier for any percentage change: - For a P% \textbf{increase}, the multiplier is \(1 + \frac{P}{100}\). - For a P% \textbf{decrease}, the multiplier is \(1 - \frac{P}{100}\). For example, a 15% decrease would have a multiplier of \(1 - 0.15 = 0.85\).

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
A multiplier is a factor that we can multiply a number by to get a new value after a percentage change. To increase a number, the multiplier must be greater than 1.
Step 2: Key Formula or Approach:
The multiplier for an increase of P% is given by the formula:
\[ \text{Multiplier} = 1 + \frac{P}{100} \] Step 3: Detailed Explanation:
Let the original number be N.
The increase is 25.3% of N, which can be written as:
\[ \text{Increase} = \frac{25.3}{100} \times N = 0.253 \times N \] The new number is the original number plus the increase:
\[ \text{New Number} = N + (0.253 \times N) \] Factoring out N, we get:
\[ \text{New Number} = N \times (1 + 0.253) \] \[ \text{New Number} = N \times 1.253 \] The multiplier is the value in the parenthesis.
Alternatively, using the formula with P = 25.3:
\[ \text{Multiplier} = 1 + \frac{25.3}{100} = 1 + 0.253 = 1.253 \] Step 4: Final Answer:
The multiplier to increase a given number by 25.3% is 1.253.