Question

49. A passenger train takes 2 hours less for a journey of 300 km if its speed
is increased by 5 km/hr from its usual speed. Find its usual speed.
​

Answer 1

Answer:

Let the usual speed of the train is x km/h.

D=300 km (Given)

Speed=

Time

Distance

Time=

x

300

After increasing the speed of the train ;

New speed is (x+5) km/h

Time=

x+5

300

Now, difference between the time taken by usual speed and after increasing speed of the train is two hours. Therefore,

x

300

−

x+5

300

=2

⇒300(

x

1

−

x+5

1

)=2

⇒(

x

2

+5x

x+5−x

)=

300

2

⇒

x

2

+5x

5

=

150

1

⇒x

2

+5x−750=0

⇒x

2

+30x−25x−750=0

⇒x(x+30)−25(x+30)=0

⇒(x+30)(x−25)=0

⇒x=25,−30

Ignore the negative value of the speed.

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