question_answer

Two trains X and Y start from Jodhpur to Jaipur and from Jaipur to Jodhpur respectively. After passing each other they take 4 hr 48 min and 3 hr 20 min to reach Jaipur and Jodhpur respectively. If X is moving at 45 km/hr, the speed of Y is:

A)  60 km/hr          

B)  58 km/hr

C)  54 km/hr          

D)  64.8km/hr

Correct Answer: C

Solution :

 Distance travelled by X in 4 hrs 48 min after they meet \[=45\,x\left( 4+\frac{48}{60} \right)\Rightarrow 45\,x\frac{24}{5}=216\,km\] Speed of train Y= x km/hr \[\Rightarrow \]Distance AM = x \[\times \] (3 hrs + 20 min) =         \[x\times \frac{10}{3}\Rightarrow \frac{10x}{3}km\] Now, Time taken to reach A by Y = Time taken to reach A by X \[\Rightarrow \frac{216}{x}\frac{\frac{10x}{3}}{45}\Rightarrow \] Shortcut method: - Speed of 2rd train (Y) = speed of 1st train (\[\times \]) \[\sqrt{Ratio\,\,of\,\,their\,time\,\,after\,\,they\,\,met.}\] \[=45\times \sqrt{\frac{\frac{24}{5}}{\frac{10}{3}}}=45\times \sqrt{\frac{24\times 3}{50}}\] \[=45\times \frac{6}{5}=\]