Calculating the Multiplier for a 25.3% Increase

This question asks us to find the specific number (multiplier) that, when multiplied by an original number, results in that number being increased by 25.3%. Let's break down how to find this multiplier.

Understanding Percentage Increase

When a number is increased by a percentage, it means we add that percentage of the original number to itself. An increase of 25.3% means we are adding 25.3% of the original value to the original value.

• The original number represents 100% of itself.
• The increase is 25.3% of the original number.
• The new total value will be the original 100% plus the increase of 25.3%.

Deriving the Multiplier

To find the multiplier, we can think about the total percentage the new number represents compared to the original. The calculation is as follows:

Total Percentage = Original Percentage + Percentage Increase

Total Percentage = $100\% + 25.3\% = 125.3\%$

This means the new number is 125.3% of the original number. To use this in calculations, we need to convert the percentage to a decimal multiplier. We do this by dividing by 100:

Multiplier = $\frac{125.3}{100} = 1.253$

Alternatively, we can use a direct formula. If the original number is N and the percentage increase is P%, the new number is calculated as:

New Number = $N \times (1 + \frac{P}{100})$

In this case, $P = 25.3$. So the multiplier is:

Multiplier = $1 + \frac{25.3}{100} = 1 + 0.253 = 1.253$

Analyzing the Options

Let's examine the given options to see which one matches our calculated multiplier:

• 12.53: This multiplier would represent an increase of $(12.53 - 1) \times 100 = 11.53 \times 100 = 1153\%$.
• 1.253: This multiplier represents an increase of $(1.253 - 1) \times 100 = 0.253 \times 100 = 25.3\%$. This matches our requirement.
• 13.53: This multiplier represents an increase of $(13.53 - 1) \times 100 = 12.53 \times 100 = 1253\%$.
• 125.3: This multiplier represents an increase of $(125.3 - 1) \times 100 = 124.3 \times 100 = 12430\%$.

Conclusion

The multiplier that increases a given number by exactly 25.3% is 1.253.