Two numbers are respectively 40% and 60% more than a third number. The ratio of first number to the second number is:

Options

A. `7:9`
B. `8:9`
C. `8:7`
D. `7:8`

Answer

To solve the problem step by step, we will denote the third number as \( x \).

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

### Step 2: Calculate the First Number
The first number is 40% more than the third number.
To find the first number, we can calculate:
\[ \text{First Number} = x + 0.40x = 1.40x \]

### Step 3: Calculate the Second Number
The second number is 60% more than the third number.
To find the second number, we can calculate:
\[ \text{Second Number} = x + 0.60x = 1.60x \]

### Step 4: Set Up the Ratio
Now, we need to find the ratio of the first number to the second number:
\[ \text{Ratio} = \frac{\text{First Number}}{\text{Second Number}} = \frac{1.40x}{1.60x} \]

### Step 5: Simplify the Ratio
The \( x \) in the numerator and denominator cancels out:
\[ \text{Ratio} = \frac{1.40}{1.60} \]
To simplify this, we can multiply both the numerator and the denominator by 100:
\[ \text{Ratio} = \frac{140}{160} \]
Now, we can simplify this fraction:
\[ \text{Ratio} = \frac{7}{8} \]

### Final Step: Conclusion
Thus, the ratio of the first number to the second number is \( 7:8 \).