A train can travel 50% faster than a car . Both start from point A at the same…
2023
A train can travel 50% faster than a car . Both start from point A at the same time and reach point B75 kms away from A t the same time . On the way , however , the train lost about 12 minutes while stopping at the stations . The speed of the car is :
- A.
105 kmph
- B.
125 kmph
- C.
120 kmph
- D.
130 kmph
Attempted by 12 students.
Show answer & explanation
Correct answer: B
Key idea: equate the car's travel time to the train's running time plus stoppage time.
Let the car's speed be x km/h. Then the train's speed is 1.5x (50% faster) = 3x/2 km/h.
Car's travel time for 75 km = 75/x hours.
Train's running time for 75 km = 75 / (3x/2) = 50/x hours. Train stoppage = 12 minutes = 0.2 hours.
Set times equal: 75/x = 50/x + 0.2
Subtract 50/x from both sides: 25/x = 0.2
So x = 25 / 0.2 = 125
Therefore the car's speed is 125 kmph.
Quick check:
With x = 125, car time = 75/125 = 0.6 h; train running time = 50/125 = 0.4 h; plus 0.2 h stoppage gives 0.6 h, matching the car's time.