Question : $\mathrm{A}$ and $\mathrm{B}$ are running on a circular track of length $1400 \;\mathrm{m}$. The speed of $\mathrm{A}$ is $33\; \mathrm{m/s}$ and the speed of $\mathrm{B}$ is $47\; \mathrm{m/s}$. They start from the same point at the same time in the opposite direction. After how much time (in seconds ) will they meet for the second time?
Option 1: $33$
Option 2: $38$
Option 3: $35$
Option 4: $32$
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Correct Answer: $35$
Solution : The relative speed of A and B $=33\;\mathrm{m/s} + 47\;\mathrm{m/s} = 80\;\mathrm{m/s}$ The time they take to meet for the first time $=\frac{1400}{80} = 17.5\;\mathrm{s}$ Since they meet every time they cover the length of the track, They will meet for the second time after another $17.5\;\mathrm{seconds}$. Therefore, A and B will meet for the 2nd time after $17.5 + 17.5 = 35\;\mathrm{seconds}$ Hence, the correct answer is $35$.
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