When an odd number of two digit is divided by an even number of two digits, then quotient is `0.625`. If the odd number is less than the even number by 5, then what is the ratio between odd number and even number?

Options

A. `5:8`
B. `8:5`
C. `6:9`
D. Cannot be determined

Answer

To solve the problem step by step, we will denote the odd number as \( x \) and the even number as \( y \).

### Step 1: Set up the equation based on the given quotient
We know that when the odd number \( x \) is divided by the even number \( y \), the quotient is \( 0.625 \). This can be expressed as:
\[ \frac{x}{y} = 0.625 \]

### Step 2: Convert the decimal to a fraction
To eliminate the decimal, we convert \( 0.625 \) into a fraction. We can write:
\[ 0.625 = \frac{625}{1000} \]

### Step 3: Simplify the fraction
Now, we simplify \( \frac{625}{1000} \) by dividing both the numerator and the denominator by their greatest common divisor (GCD), which is \( 125 \):
\[ \frac{625 \div 125}{1000 \div 125} = \frac{5}{8} \]
Thus, we have:
\[ \frac{x}{y} = \frac{5}{8} \]

### Step 4: Express \( x \) in terms of \( y \)
From the ratio \( \frac{x}{y} = \frac{5}{8} \), we can express \( x \) in terms of \( y \):
\[ x = \frac{5}{8}y \]

### Step 5: Use the condition that \( x \) is less than \( y \) by 5
According to the problem, the odd number \( x \) is less than the even number \( y \) by 5. This gives us the equation:
\[ y - x = 5 \]
Substituting \( x \) from the previous step:
\[ y - \frac{5}{8}y = 5 \]

### Step 6: Solve for \( y \)
To solve for \( y \), we first combine the terms on the left:
\[ \frac{3}{8}y = 5 \]
Now, multiply both sides by \( \frac{8}{3} \):
\[ y = 5 \cdot \frac{8}{3} = \frac{40}{3} \]

### Step 7: Find \( x \)
Now that we have \( y \), we can find \( x \):
\[ x = \frac{5}{8}y = \frac{5}{8} \cdot \frac{40}{3} = \frac{200}{24} = \frac{25}{3} \]

### Step 8: Find the ratio \( x:y \)
Now we have both \( x \) and \( y \):
\[ x = \frac{25}{3}, \quad y = \frac{40}{3} \]
The ratio \( x:y \) can be expressed as:
\[ \frac{x}{y} = \frac{\frac{25}{3}}{\frac{40}{3}} = \frac{25}{40} = \frac{5}{8} \]

### Final Answer
Thus, the ratio between the odd number and the even number is:
\[ \text{Ratio } x:y = 5:8 \]