Two numbers are `25% and 15%` less than the third number respectively. First number is what percent less than the second number?

Options

A. `11.76`
B. `13.5`
C. `17.8`
D. `20.4`

Answer

To solve the problem step by step, we will follow these calculations:

1. **Assume the third number**: Let's denote the third number as \( x \).

2. **Calculate the first number**: The first number is 25% less than the third number. Therefore, the first number can be expressed as:
\[ \text{First Number} = x - 0.25x = 0.75x \]

3. **Calculate the second number**: The second number is 15% less than the third number. Thus, the second number can be expressed as:
\[ \text{Second Number} = x - 0.15x = 0.85x \]

4. **Find the difference between the first and second numbers**: We need to find how much less the first number is than the second number. The difference is:
\[ \text{Difference} = \text{Second Number} - \text{First Number} = 0.85x - 0.75x = 0.10x \]

5. **Calculate the percentage difference**: To find out what percent the first number is less than the second number, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Difference}}{\text{Second Number}} \right) \times 100 \]
Substituting the values we have:
\[ \text{Percentage} = \left( \frac{0.10x}{0.85x} \right) \times 100 \]

6. **Simplify the expression**: The \( x \) cancels out:
\[ \text{Percentage} = \left( \frac{0.10}{0.85} \right) \times 100 \]

7. **Calculate the final value**:
\[ \text{Percentage} = \left( \frac{10}{85} \right) \times 100 = \frac{1000}{85} \approx 11.76\% \]

Thus, the first number is approximately **11.76% less than the second number**.