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

Concept: A multiplier is a factor applied to a number to reflect a percentage change. For increases, the multiplier exceeds 1.
Formula: The multiplier for a P% increase is calculated as:
\[ \text{Multiplier} = 1 + \frac{P}{100} \]Explanation: Let the original number be N. An increase of 25.3% is represented as:
\[ \text{Increase} = \frac{25.3}{100} \times N = 0.253 \times N \]The new number is the sum of the original number and the increase:
\[ \text{New Number} = N + (0.253 \times N) \]Factoring out N gives:
\[ \text{New Number} = N \times (1 + 0.253) \]\[ \text{New Number} = N \times 1.253 \]The multiplier is the factor (1.253). Using the formula with P = 25.3:
\[ \text{Multiplier} = 1 + \frac{25.3}{100} = 1 + 0.253 = 1.253 \]Result: The multiplier for a 25.3% increase is 1.253.