1. In the chromyl chloride test, chloride ion gives chromyl chloride, and after further treatment a yellow solution containing chromium in a high oxidation state is obtained.

2. On acidification and addition of amyl alcohol with $10\%\,\mathrm{H_2O_2}$, the blue organic layer is due to formation of chromium pentoxide, written as: $\mathrm{CrO_5}$

3. Let the oxidation state of chromium in $\mathrm{CrO_5}$ be $x$.

4. In $\mathrm{CrO_5}$, the structure contains:

• one oxo oxygen: oxidation number $-2$
• two peroxide groups $(-\mathrm{O-O}-)$, i.e. four oxygens each with oxidation number $-1$

So total oxidation contribution of oxygen is: $(-2) + 4(-1) = -6$

5. Since the molecule is neutral: $x + (-6) = 0$ $x = +6$

6. Therefore, the oxidation state of chromium in chromium pentoxide is: $\boxed{+6}$

7. Checking options:

• A: $+6$ ✅
• B: $+5$ ❌
• C: $+3$ ❌
• D: $+10$ ❌

Hence, the correct option is A.