JEE Main 2024 — Probability Question with Solution

A company has two plants $$A$$ and $$B$$ to manufacture motorcycles. $$60\%$$ motorcycles are manufactured at plant $$A$$ and the remaining are manufactured at plant $$B.80\%$$ of the motorcycles manufactured at plant $$A$$ are rated of the standard quality, while $$90\%$$ of the motorcycles manufactured at plant $$B$$ are rated of the standard quality. A motorcycle picked up randomly from the total production is found to be of the standard quality. If $$p$$ is the probability that it was manufactured at plant $$B$$, then $$126p$$ is