Two numbers are 32% and 48% more than a third number. What percentage (correct to two decimal places) is the second number of the first?

Options

A. `89.19%`
B. `112.12%`
C. `102.12%`
D. `150. 12%`

Answer

To solve the problem step by step, we need to find the percentage of the second number with respect to the first number.

### Step 1: Define the third number
Let the third number be \( x \).

### Step 2: Calculate the first number
The first number is 32% more than the third number. Therefore, we can express the first number as:
\[ \text{First number} = x + 0.32x = 1.32x \]

### Step 3: Calculate the second number
The second number is 48% more than the third number. Thus, we can express the second number as:
\[ \text{Second number} = x + 0.48x = 1.48x \]

### Step 4: Find the percentage of the second number with respect to the first number
To find what percentage the second number is of the first number, we use the formula:
\[ \text{Percentage} = \left( \frac{\text{Second number}}{\text{First number}} \right) \times 100 \]
Substituting the values we found:
\[ \text{Percentage} = \left( \frac{1.48x}{1.32x} \right) \times 100 \]

### Step 5: Simplify the expression
The \( x \) in the numerator and denominator cancels out:
\[ \text{Percentage} = \left( \frac{1.48}{1.32} \right) \times 100 \]

### Step 6: Calculate the fraction
Now we calculate \( \frac{1.48}{1.32} \):
\[ \frac{1.48}{1.32} \approx 1.121212 \]

### Step 7: Multiply by 100 to get the percentage
\[ \text{Percentage} \approx 1.121212 \times 100 \approx 112.12 \]

### Step 8: Round to two decimal places
Thus, the percentage of the second number with respect to the first number is:
\[ \text{Percentage} \approx 112.12\% \]

### Final Answer
The second number is approximately **112.12%** of the first number.

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