The grammatical error in the sentence "BK sir and SCS sir teach physics and play badminton with each other" is the lack of a parallel structure.

Here's why:

• The sentence implies that BK sir and SCS sir both teach physics and both play badminton.
• To properly convey this with parallel structure, we need to ensure the verbs associated with each subject are correctly paired.

Possible Corrections:

1. Option 1: "BK sir and SCS sir teach physics and play badminton." (This assumes they do both activities together.)
2. Option 2: "BK sir and SCS sir teach physics and play badminton with each other." can be interpreted as BK Sir and SCS Sir teach physics (together) and play badminton with each other.
3. Option 3: "BK sir teaches physics, and SCS sir plays badminton with him." (This separates the activities.)