Two numbers are 20% and 40% more tha the third number respectively. The ratio of the first and second number is

Options

A. `7:6`
B. `7:5`
C. `6:7`
D. `5:7`

Answer

To solve the problem of finding the ratio of two numbers that are 20% and 40% more than a third number, we can follow these steps:

### Step-by-Step Solution:

1. **Define the Third Number**:
Let the third number be \( x \).

2. **Calculate the First Number**:
The first number is 20% more than the third number.
\[ \text{First Number} = x + 0.2x = 1.2x \]

3. **Calculate the Second Number**:
The second number is 40% more than the third number.
\[ \text{Second Number} = x + 0.4x = 1.4x \]

4. **Set Up the Ratio**:
We need to find the ratio of the first number to the second number.
\[ \text{Ratio} = \frac{\text{First Number}}{\text{Second Number}} = \frac{1.2x}{1.4x} \]

5. **Simplify the Ratio**:
The \( x \) in the numerator and denominator cancels out:
\[ \frac{1.2}{1.4} = \frac{12}{14} = \frac{6}{7} \]

6. **Final Result**:
Therefore, the ratio of the first number to the second number is \( 6:7 \).