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A train starts at $7$ a.m. from $A$ towards $B$ with a speed of $50$ km/hr. Another train from $B$ starts at $8$ a.m. with a speed of $60$ km/hr towards $A$. Both of them meet at $10$ a.m. at $C$. The ratio of the distances $AC$ to $BC$ is :

1. $4:5$
2. $5:4$
3. $5:6$
4. $6:5$

Train $A:$ Speed $= 50\;km/hr,$ Time $= 3\;hr$

Distance from $A$ to $C = 50 \times 3 = 150\;km$

Train $B:$ Speed $= 60\;km/hr,$ Time $= 2\;hr$

Distance from $B$ to $C = 60 \times 2 = 120\;km$

$\therefore$ The required ratio $= \dfrac{AC}{BC} = \dfrac{150}{120} = \dfrac{5}{4}$

Hence, the ratio of the distances $AC$ to $BC$ is $= 5:4.$

So, the correct answer is $(B).$
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