A train runs first 75 km at a certain uniform speed and next 90 km at an average speed of 10 km/h more than the normal speed. If it takes 3 hour to complete the journey, then how much time will the train takes to cover 300 km with normal speed ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is option 4 i.e. 6 hours
Given :
A train runs first 75 km at a certain uniform speed
Next 90 km at an average speed of 10 km/h more than the normal speed
Total time taken = 3 hours
Formula used :
Speed = Distance/time ----- (1)
Calculations :
Let the speed of train be x
Speed of train when it travels 90km
Total time = Time taken to travel 75km + Time taken to travel 90km
⇒ 3 = (75/x) + 90/(x + 10)
⇒ 3(x2 + 10x) = 75x + 750 + 90x
⇒ 3x2 + 30x = 165x + 750
⇒ 3x2 - 135x - 750 = 0
⇒ x2 - 45x - 250 = 0
⇒ x2 - 50x + 5x - 250 = 0
⇒ x(x - 50) + 5(x - 50) = 0
⇒ x = 50, -5
Speed of the train = x = 50kmph
Time taken to travel 300km
Using equation (1)
⇒ 300/50
⇒ 6 hours
Hence, Time taken to travel 300km with normal speed is 6 hours.