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: Concept Definition:
A multiplier is a numerical factor used to determine a new value after a percentage change. For an increase, the multiplier must exceed 1.
Step 2: Calculation Method:
The formula for calculating the multiplier for a P% increase is:
\[ \text{Multiplier} = 1 + \frac{P}{100} \]Step 3: Step-by-Step Calculation:
Let the initial value be N.
A 25.3% increase on N is calculated as:
\[ \text{Increase Amount} = \frac{25.3}{100} \times N = 0.253 \times N \]The resulting value is the original value plus the increase:
\[ \text{New Value} = N + (0.253 \times N) \]By factoring out N, we get:
\[ \text{New Value} = N \times (1 + 0.253) \]\[ \text{New Value} = N \times 1.253 \]The multiplier is the factor (1.253) multiplying N.
Alternatively, applying the formula with P = 25.3:
\[ \text{Multiplier} = 1 + \frac{25.3}{100} = 1 + 0.253 = 1.253 \]Step 4: Conclusion:
The multiplier required to increase a value by 25.3% is 1.253.