Two trains A and B start at the same time from X and Y respectively and move towards each other. After they cross each other, trains A and B take 16 hours and 25 hours respectively to reach their destinations. If the speed of train A is 30 km/hr, what is the distance between X and Y?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 1080 km
If two trains meet and then take \(t_{1}\) and \(t_{2}\) hours to finish, their speeds are in the ratio \(\sqrt{t_{2}}:\sqrt{t_{1}}\). After the meeting, each train covers the part that the other train covered before it.
Speed of A : speed of B \(=\sqrt{25}:\sqrt{16}=5:4\)
Speed of B \(\displaystyle =30\times\frac{4}{5}=24\) km/hr
After the meeting, A covers B’s part: \(30\times16=480\) km
B took \(\displaystyle \frac{480}{24}=20\) hr to cover that part, so they met after 20 hr
Distance XY \(=(30+24)\times20=54\times20=1080\) km