Question

A train travels some distance at a constant speed. If the speed of the train would have increased by 15 km/hr, then it would have required 2 hours less. But if the speed of the train would have decreased by 5 km then to cover the same distance it would have required 1 hour more. Find the distance covered by the train. 

(1) 120 km 

(2) 240 km 

(3) 360 km 

(4) 400 km

Answer 1

Correct option is (3) 360 km

Speed x km/hr distance = y km 

Speed = (x + 15)

\(\frac{\text{y}}{\text{x+5}}=\frac{\text{y}}{\text{x}}\) - 2

⇒ xy = (x + 15) (y - 2x)

⇒ xy = xy + 15y - 2x² - 30x

⇒ 15y = 2x² + 30x

Speed = (x – 15) km/hr

\(\)\(\frac{\text{y}}{\text{x-5}}=\frac{\text{y}}{\text{x}}\) + 1

xy = (x - 5) (y + 5)

⇒ xy = xy + x² - 5y - 5x

⇒ 5y = x² - 5x

⇒ 15y = 3x² - 15x

∴ 3x² - 15x = 2x² + 30x

⇒ x² - 45x = 0

x = 0, x = 45

∴ y = \(\frac{(45)^2}{5}\) - 45 = 405 - 45 = 360 km