Two numbers are respectively 20% and 50% of a third number. What per cent is the first number of the second?

Options

A. 0.1
B. 0.2
C. 0.3
D. 0.4

Answer

To solve the problem step by step, we can follow these instructions:

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

### Step 2: Calculate the first number
The first number is 20% of the third number. Therefore, we can express it as:
\[ \text{First number} = 20\% \text{ of } x = \frac{20}{100} \times x = 0.2x \]

### Step 3: Calculate the second number
The second number is 50% of the third number. Thus, we can express it as:
\[ \text{Second number} = 50\% \text{ of } x = \frac{50}{100} \times x = 0.5x \]

### Step 4: Find the percentage of the first number with respect to the second number
We need to find what percentage the first number is of the second number. This can be calculated using the formula:
\[ \text{Percentage} = \left( \frac{\text{First number}}{\text{Second number}} \right) \times 100 \]
Substituting the values we calculated:
\[ \text{Percentage} = \left( \frac{0.2x}{0.5x} \right) \times 100 \]

### Step 5: Simplify the expression
The \( x \) in the numerator and denominator cancels out:
\[ \text{Percentage} = \left( \frac{0.2}{0.5} \right) \times 100 \]
Now, simplifying \( \frac{0.2}{0.5} \):
\[ \frac{0.2}{0.5} = \frac{2}{5} \]
So we have:
\[ \text{Percentage} = \left( \frac{2}{5} \right) \times 100 \]

### Step 6: Calculate the final percentage
Now, calculating \( \frac{2}{5} \times 100 \):
\[ \frac{2 \times 100}{5} = \frac{200}{5} = 40 \]

### Final Answer
Thus, the first number is 40% of the second number.

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