Two numbers are respectively 20% and 50% more than a 3rd number.What is the percentage of 2nd with respect to 1st?

Options

A. `125%`
B. `90%`
C. `80%`
D. `75%`

Answer

To solve the problem step by step, we will define the three numbers and calculate the required percentage.

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

### Step 2: Calculate the first number
The first number \( X \) is 20% more than the third number \( Z \).
This can be expressed as:
\[ X = Z + 0.2Z = 1.2Z \]

### Step 3: Calculate the second number
The second number \( Y \) is 50% more than the third number \( Z \).
This can be expressed as:
\[ Y = Z + 0.5Z = 1.5Z \]

### Step 4: Find the relationship between the first and second numbers
Now, we need to find out what percentage the second number \( Y \) is of the first number \( X \). This can be expressed as:
\[ \text{Percentage of } Y \text{ with respect to } X = \left( \frac{Y}{X} \right) \times 100 \]

### Step 5: Substitute the values of \( Y \) and \( X \)
Substituting the values we found:
\[ \frac{Y}{X} = \frac{1.5Z}{1.2Z} \]
The \( Z \) cancels out:
\[ \frac{Y}{X} = \frac{1.5}{1.2} \]

### Step 6: Simplify the fraction
Now, simplify \( \frac{1.5}{1.2} \):
\[ \frac{1.5}{1.2} = \frac{15}{12} = \frac{5}{4} \]

### Step 7: Convert to percentage
Now, converting \( \frac{5}{4} \) to percentage:
\[ \frac{5}{4} \times 100 = 125\% \]

### Final Answer
Thus, the second number \( Y \) is 125% of the first number \( X \).

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