Question

$A$ train takes $2$ hours less for a journey of $300km$ if its speed is increased by $5km$ h from its usual speed. Find the usual speed of the train.

• A. $65$ km/hr
• B. $55$ km/hr
• C. $25$ km/hr
• D. $5$ km/hr

Answer 1

Answer: (C)

$25$ km/hr

Let the usual speed of the train be 'x' km/hr.

A.T.Q.

300/x – 300/(x+5) = 2

=> 300(x+5) – 300x / x(x+5) = 2

=> 300x + 1500 – 300x / x² + 5x = 2

=> 2(x² + 5x) = 1500

=> 2x² + 10x – 1500 = 0

=> x² + 5x – 750 = 0

=> x² + 30x – 25x – 750 = 0

=> x(x + 30) – 25 (x + 30) = 0

=> (x+30) (x–25) = 0

=> x = –30 or x = 25

Speed can't be negative. So, x = –30 is inappropriate.

Thus, the usual speed of the train is 25 km/hr.