Explanation:

- Given ratios:

- $p:q=4:5$

- $q:r=3:4$

- $r:s=2:5$

- Find $p:s$.

1. Step 1:

- Calculate $p:r$ using $p:q$ and $q:r$.

- Multiply corresponding parts: $p:r=4\times 3:5\times 4=12:20$.

2. Step 2:

- Calculate $p:s$ using $p:r$ and $r:s$.

- Multiply corresponding parts:

- $r:s=20:40$

- Thus, $p:s=12\times 2:20\times 5=24:100$.

- Simplify $p:s=6:25$.

- Answer:

- 6 : 25 $✓$