Question : Two trains start at the same time from Aligarh and Delhi and proceed towards each other at the rate of 14 km and 21 km per hour respectively. When they meet, it is found that one train has travelled 70 km more than the other. The distance between the two stations is:
Option 1: 350 km
Option 2: 210 km
Option 3: 300 km
Option 4: 140 km
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Correct Answer: 350 km
Solution : Let the distance when they met be $X$. During the whole Journey, the time remains same for the both trains. So, $\frac{\text{Speed of Delhi train}} {\text{Speed of Aligarh train}} = \frac{\text{Distance covered by Delhi train}}{\text{Distance covered by Aligarh train}}$ $⇒\frac{21}{14} = \frac{(X +70)}{X}$ $⇒21X = 14X + 980$ $⇒7X = 980$ $\therefore X = 140$ So, total Distance = $2X + 70 = 2 × (140 + 70) = 350$ km Hence, the correct answer is 350 km.
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