A survey of Year 8 students shows that $$ 40 \% $$ of students walk to school, one-sixth ride their bike and the remainder catch the bus. 2 What is the ratio of students who walk to those who ride to those who catch the bus, among this year level? A $$ 0.4: 0.17: 0.43 $$ B $$ 2: 1: 5 $$ C $$ 12: 5: 13 $$ D $$ 40: 1: 5 $$

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To find the ratio of students who walk, ride their bike, and catch the bus, we start by determining the proportions of each group based on the information given.

1. **Walking to school**: 
   - $$ 40\% $$ of students walk to school. This can be expressed as a fraction: 
   $$
   0.4
   $$

2. **Riding a bike**: 
   - One-sixth of the students ride their bike. This can be expressed as a fraction:
   $$
   \frac{1}{6} \approx 0.1667
   $$

3. **Catching the bus**: 
   - The remainder of the students catch the bus. To find this, we first calculate the total percentage of students who walk and ride their bike:
   $$
   40\% + \frac{1}{6} = 0.4 + 0.1667 \approx 0.5667
   $$
   - Therefore, the percentage of students who catch the bus is:
   $$
   1 - 0.5667 \approx 0.4333
   $$

Now we have the proportions:
- Walking: $$ 0.4 $$
- Riding: $$ \frac{1}{6} \approx 0.1667 $$
- Catching the bus: $$ 0.4333 $$

Next, we convert these proportions into a ratio. To do this, we can express each proportion as a fraction of a common denominator. The least common multiple of the denominators (1, 6, and 1) is 6.

- Walking: 
$$
0.4 = \frac{40}{100} = \frac{24}{60} \quad (\text{multiply by } 1.5)
$$
- Riding: 
$$
\frac{1}{6} = \frac{10}{60}
$$
- Catching the bus: 
$$
0.4333 \approx \frac{26}{60} \quad (\text{multiply by } 1.5)
$$

Now we can express the ratios:
- Walking: $$ 24 $$
- Riding: $$ 10 $$
- Catching the bus: $$ 26 $$

Thus, the ratio of students who walk to those who ride to those who catch the bus is:
$$
24 : 10 : 26
$$

To simplify this ratio, we can divide each term by 2:
$$
12 : 5 : 13
$$

Thus, the final ratio of students who walk to those who ride to those who catch the bus is:
$$
\boxed{12 : 5 : 13}
$$

The correct answer is **C** $$ 12: 5: 13 $$.
The ratio of students who walk to those who ride to those who catch the bus is 12:5:13.

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