question_answer

Two places P and Q are 162 km apart. A train leaves P for Q and simultaneously another train leaves Q for P. They meet at the end of 6 h. If the former train travels 8 km/h faster than the other, then speed of train from Q is [SSC CGL Tier II, 2015]

A) \[9\frac{1}{2}km/h\]

B) \[12\frac{5}{6}km/h\]

C) \[8\frac{1}{2}km/h\]

D) \[10\frac{5}{6}km/h\]

Correct Answer: A

Solution :

[a] Let the speed of train V km/h, which leaves from place point Q and both trains will meet at point D. Then, PD = x km           \[\left[ \therefore \text{Speed=}\frac{\text{Distsnce}}{\text{Time}} \right]\] \[V+\frac{8}{6}\]             \[\therefore \]      \[x=6\,(V+8)\]                           (i)             and       \[V=\frac{162-x}{6}\]             \[\Rightarrow \]   \[6V=162-6\,(V+8)\]             \[\Rightarrow \]   \[6V=162-6\,(V+8)-48\]             \[\Rightarrow \]   \[12V=114\]             \[\therefore \]      \[V=\frac{114}{12}=9\frac{6}{12}=9\frac{1}{2}\text{km/h}\]