Two numbers are respectively 20% and 50% more than a third number. The ratio of the two numbers is

Options

A. `2:5`
B. `3:5`
C. `4:5`
D. `6:7`

Answer

To solve the problem step by step, let's define the third number as \( x \).

**Step 1: Define the first number.**
The first number is 20% more than the third number \( x \).
\[ \text{First number} = x + 0.2x = 1.2x \]

**Step 2: Define the second number.**
The second number is 50% more than the third number \( x \).
\[ \text{Second number} = x + 0.5x = 1.5x \]

**Step 3: Write the ratio of the two numbers.**
We need to find the ratio of the first number to the second number.
\[ \text{Ratio} = \frac{\text{First number}}{\text{Second number}} = \frac{1.2x}{1.5x} \]

**Step 4: Simplify the ratio.**
The \( x \) in the numerator and denominator cancels out:
\[ \text{Ratio} = \frac{1.2}{1.5} \]
To simplify \( \frac{1.2}{1.5} \), we can multiply both the numerator and denominator by 10 to eliminate the decimal:
\[ \frac{1.2 \times 10}{1.5 \times 10} = \frac{12}{15} \]
Now, simplify \( \frac{12}{15} \) by dividing both the numerator and denominator by 3:
\[ \frac{12 \div 3}{15 \div 3} = \frac{4}{5} \]

**Final Answer:**
The ratio of the two numbers is \( 4:5 \).

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