We have two different liquids `A` and `B` whose relative densities are `0.75` and `1.0`, respectively. If we dip solid objects `P` and `Q` having relative densities `0.6` and `0.9` in these liquids, then

Options

A. `P` floats in `A` and `Q` sinks in `B`
B. `P` sinks in `A` and `Q` floats in `B`
C. `P` floats in `B` and `Q` sinks in `A`
D. `P` sinks in `B` and `Q` floats in `A`

Explanation

To solve the problem, we need to analyze the behavior of the solid objects P and Q when immersed in the liquids A and B based on their relative densities.

### Step-by-Step Solution:

1. **Identify the Relative Densities**:
- Liquid A has a relative density of 0.75.
- Liquid B has a relative density of 1.0 (which is the density of water).
- Object P has a relative density of 0.6.
- Object Q has a relative density of 0.9.

2. **Determine the Behavior of Object P in Liquid A**:
- The density of liquid A (0.75) is greater than the density of object P (0.6).
- According to the principle of buoyancy, if the density of the liquid is greater than the density of the object, the object will float.
- Therefore, **Object P will float in Liquid A**.

3. **Determine the Behavior of Object Q in Liquid B**:
- The density of liquid B (1.0) is greater than the density of object Q (0.9).
- Again, since the density of the liquid is greater than the density of the object, object Q will float in liquid B.
- Therefore, **Object Q will float in Liquid B**.

4. **Determine the Behavior of Object P in Liquid B**:
- The density of liquid B (1.0) is greater than the density of object P (0.6).
- Thus, object P will float in liquid B as well.
- Therefore, **Object P will float in Liquid B**.

5. **Determine the Behavior of Object Q in Liquid A**:
- The density of liquid A (0.75) is less than the density of object Q (0.9).
- Since the density of the liquid is less than the density of the object, object Q will sink in liquid A.
- Therefore, **Object Q will sink in Liquid A**.

### Conclusion:
- Object P floats in both Liquid A and Liquid B.
- Object Q sinks in Liquid A but floats in Liquid B.

### Final Answer:
- The correct statements about the objects in the liquids are:
- P floats in A (True)
- P floats in B (True)
- Q sinks in A (True)
- Q floats in B (True)