Question : From point H, at 6:30 pm, a train starts moving towards point K at the speed of 90 km/hr. Another train starts moving from point K at 7:30 p.m. towards point H at the speed of 72 km/hr. Both trains meet at 11:30 p.m. at point J. What is the ratio of the distance HJ and KJ?
Option 1: 25 : 16
Option 2: 5 : 16
Option 3: 36 : 25
Option 4: 31 : 19
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Correct Answer: 25 : 16
Solution :
Given, H to K = 6:30 pm at 90 km/hr
K to H = 7: 30 pm at 72 km/hr
J = 11: 30 pm
The time between 6:30 pm and 11:30 pm = 5 hours
⇒ Distance between point H and J = 90 × 5 = 450 km
The time between 7:30 pm and 11:30 pm = 4 hours
⇒ Distance between points K and J = 72 × 4 = 288 km
$\therefore$ Ratio of distance HJ and KJ = 450 : 288 = 25 : 16
Hence, the correct answer is 25 : 16.
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