A tram overtakes 2 persons X and Y walking at an average speed of 3 km/hr and 4 km/hr in the same direction and completely passes them in 8 seconds and 9 seconds respectively. What is the length of the tram ?
- A15 m
- B18 m
- C20 mCorrect
- D24 m
Explanation
Let the length of the tram be L meters and its speed be V km/hr.
When a tram passes a moving person, the relative speed is the difference between their speeds because they are moving in the same direction.
For the first person X: Relative speed = V minus 3 km/hr. Converting this to meters per second: (V minus 3) multiplied by 5/18. Distance covered is the length of the tram (L). L = (V minus 3) multiplied by 5/18 multiplied by 8 seconds. This simplifies to: L = (V minus 3) multiplied by 20/9.
For the second person Y: Relative speed = V minus 4 km/hr. L = (V minus 4) multiplied by 5/18 multiplied by 9 seconds. This simplifies to: L = (V minus 4) multiplied by 5/2.
Equating the two expressions for L: (V minus 3) multiplied by 20/9 = (V minus 4) multiplied by 5/2. Multiply both sides by 18 to remove denominators: (V minus 3) multiplied by 40 = (V minus 4) multiplied by 45. 40V minus 120 = 45V minus 180. 5V = 60. V = 12 km/hr.
Now, substitute V = 12 into the expression for L: L = (12 minus 4) multiplied by 5/2. L = 8 multiplied by 2.5. L = 20 meters.
The length of the tram is 20 meters. Thus, option C is correct.
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