p-cresol reacts with chloroform in alkaline medium to give the compound A which adds hydrogen cyanide to form, the compound B. The latter on acidic hydrolysis gives chiral carboxylic acid. The structure of the carboxylic acid is

The sequence involves three well-known reactions of aromatic aldehydes and ketones.
Step-1 : Reimer-Tiemann formylation of a phenol.
Step-2 : Cyanohydrin formation (nucleophilic addition of $$HCN$$).
Step-3 : Acidic hydrolysis of the nitrile group to a carboxylic acid.

Step 1 : Preparation of compound A
In the Reimer-Tiemann reaction, phenols treated with $$CHCl_3$$ and aqueous $$KOH$$ are ortho-formylated:

$$\require{mhchem}$$ $$\ce{p-CH_3-C_6H_4-OH\ (p\text{-cresol})\xrightarrow[H_2O]{CHCl_3/KOH} \ 2-HO-3-CH_3-C_6H_3-CHO}$$

Because the para position is blocked by $$CH_3$$, the formyl group enters the ortho position relative to $$OH$$. Thus, compound A is $$2\text{-hydroxy-5-methylbenzaldehyde}$$ (also called 4-methyl-salicylaldehyde).

Step 2 : Formation of compound B
An aldehyde adds hydrogen cyanide across the $$C=O$$ bond to give a cyanohydrin:

$$ \ce{2-HO-5-CH_3-C_6H_3-CHO + HCN \longrightarrow 2-HO-5-CH_3-C_6H_3-CH(OH)-CN}\quad(\text{compound B}) $$

The carbon that was originally the aldehydic carbon now bears four different groups ($$H$$, $$OH$$, $$CN$$, and the aryl group), so B already possesses a chiral centre.

Step 3 : Acidic hydrolysis of B
On heating the cyanohydrin with dilute mineral acid, the $$-CN$$ group is converted into $$-COOH$$ without affecting the adjacent $$OH$$ group:

$$ \ce{2-HO-5-CH_3-C_6H_3-CH(OH)-CN \xrightarrow[\Delta]{H_3O^+} 2-HO-5-CH_3-C_6H_3-CH(OH)-COOH} $$

The product is $$2\text{-hydroxy-2-(2-hydroxy-5-methylphenyl)acetic acid}$$, commonly described as a 5-methyl-mandelic acid analogue. The $$\alpha$$-carbon (the one bearing $$OH$$ and $$COOH$$) remains attached to four different groups, hence the acid is chiral, exactly as stated in the problem.

The structure corresponds to Option B.

Answer : Option B which is 2-hydroxy-2-(2-hydroxy-5-methylphenyl)acetic acid.