Question
Download Solution PDFThe speed of Train E is 25% greater than that of Train B, while Train F moves 25% faster than Train A. Sum of speed of train A and B is 108 km/hr. If Trains E and F cross each other while traveling in the opposite direction in 96 seconds, and the ratio of their lengths is 3 : 2, what is the length of Train F?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCalculation
Speed of Train E is 25% greater than Train B
→ Speed of E = 1.25B
Speed of Train F is 25% greater than Train A
→ Speed of F = 1.25A
Sum of speed of Train A and B = 108 km/h
→ A + B =108
Trains E and F cross each other in 96 seconds while moving in opposite directions
Ratio of lengths of E : F = 3 : 2
→ Let lengths be: E = 3x, F = 2x
→ So total distance to cross = 5x
Time = 96 seconds
So, (A + B) =108 ---------Equation (1)
Then:
Speed of E = 1.25b
Speed of F = 1.25a
So relative speed when they cross each other =
[1.25a + 1.25b] = 1.25(a + b) =1.25 × 108 = 135 km/h = [135 × [5/18] = 37.5 m/s
Distance=Speed × Time = 37.5 × 96 = 3600 meters
But distance = E + F = 5x
So, 5x=3600
⇒ x = 3600 / 5 = 720
Train F = 2x = 2 × 720 = 1440 meters
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