Question

A passenger train takes two hours less for a journey of 300 km if its speed is increased by 5 km/hr from its normal speed. the normal speed is:

Answer 1

$\textbf{Answer}$

Suppose normal speed is x km/h
$\textbf{Total distance = 300 km}$
$\textbf{Time = Distance/Speed}$
Usual time taken = 300/x hour

Now,if speed of train increases by 5,it take 2 hours less to travel the same distance.
=> Speed = x+5 km/hour
Time = 300/(x+5) hour

$\textbf{According to the question,}$

(300/x) - 2 = 300/(x+5)

=> (300/x) - (300)/(x+5) = 2

=> (300x + 1500 - 300x)/(x)(x+5) = 2

=> 1500 = 2x^2 + 10x

=> x^2 + 5x - 750 = 0

=> x^2 + 30x - 25x - 750 = 0

=> x(x + 30) - 25(x + 30) = 0

=> (x - 25) (x + 30) = 0

=> x = 25 or x = -30

Since speed can not be negative,
=> x = 25

$\textbf{Normal speed is 25 km/hour}$

$\textbf{Hope My Answer Helped}$
$\textbf{Thanks}$

Answer 2

Suppose normal speed is x km/h
\textbf{Total distance = 300 km}Total distance = 300 km 
\textbf{Time = Distance/Speed}Time = Distance/Speed 
Usual time taken = 300/x hour

Now,if speed of train increases by 5,it take 2 hours less to travel the same distance.
=> Speed = x+5 km/hour
Time = 300/(x+5) hour

\textbf{According to the question,}According to the question, 

(300/x) - 2 = 300/(x+5)

=> (300/x) - (300)/(x+5) = 2

=> (300x + 1500 - 300x)/(x)(x+5) = 2

=> 1500 = 2x^2 + 10x

=> x^2 + 5x - 750 = 0

=> x^2 + 30x - 25x - 750 = 0

=> x(x + 30) - 25(x + 30) = 0

=> (x - 25) (x + 30) = 0

=> x = 25 or x = -30

Since speed can not be negative,
=> x = 25 

\textbf{Normal speed is 25 km/hour}Normal speed is 25 km/hour