JEE MAIN - Mathematics (2024 - 6th April Morning Shift - No. 20)
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 $$126 p$$ is
54
66
56
64
Explanation
$$\begin{aligned} & P(\text { standard automobile from } A)=\frac{6}{10} \times \frac{8}{10}=\frac{12}{25} \\ & P(\text { standard automobile from } B)=\frac{4}{10} \times \frac{9}{10}=\frac{9}{25} \end{aligned}$$
$$\begin{aligned} & \text { Required Probability } \frac{\frac{9}{25}}{\frac{12}{25}+\frac{9}{25}} \\ & P=\frac{9}{21}=\frac{3}{7} \end{aligned}$$
So, $$126 P=126 \times \frac{3}{7}=54$$
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