Explanation:

- Cycling: Sudhin cycles at 8.5 km/h for 4 hours. This covers a distance of \(8.5 \times 4 = 34\) km.

- Auto: He then travels by auto at 20 km/h for 1.5 hours, covering \(20 \times 1.5 = 30\) km.

- Walking: He walks at 4 km/h for y hours, covering \(4y\) km.

- Total Distance: The entire journey covers \(34 + 30 + 4y\) km.

- Time Travelled: Total time is \(4 + 1.5 + y\) hours.

- Average Speed Equation: Overall average speed is given as 10 km/h:

$$

\frac{34 + 30 + 4y}{4 + 1.5 + y} = 10

$$

- Solve:

$$

64 + 4y = 10(5.5 + y)

$$

$$

64 + 4y = 55 + 10y

$$

$$

64 - 55 = 10y - 4y

$$

$$

9 = 6y

$$

$$

y = \frac{9}{6} = 1.5

$$

- Correct Option: The correct option is option 3: 1.5.