The ratio of 8 books to 20 books is :
a. `2:5`
a. `5:2`
c. `4:5`
d. `5:4`

Answer

To solve the question regarding the ratio of 8 books to 20 books, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Ratio**:
The ratio of two quantities, in this case, books, is expressed as the fraction of the first quantity to the second quantity. Here, we need to find the ratio of 8 books to 20 books.

2. **Writing the Ratio**:
We can express the ratio of 8 books to 20 books as:
\[ \text{Ratio} = \frac{8}{20} \]

3. **Simplifying the Fraction**:
To simplify the fraction \(\frac{8}{20}\), we need to find the greatest common divisor (GCD) of 8 and 20. The GCD of 8 and 20 is 4. Now, we divide both the numerator and the denominator by their GCD:
\[ \frac{8 \div 4}{20 \div 4} = \frac{2}{5} \]

4. **Expressing the Simplified Ratio**:
The simplified ratio can be written as:
\[ 2:5 \]

5. **Choosing the Correct Option**:
Now, we compare our result with the given options:
- a. \(2:5\)
- b. \(5:2\)
- c. \(4:5\)
- d. \(5:4\)

The correct answer is option (a) \(2:5\).

### Final Answer:
The ratio of 8 books to 20 books is \(2:5\).