A train covers a distance of 300 km at a uniform speed. If the speed of the train is
increased by 5 km/hour, it takes 2 hours less in the journey. Find the original speed of
the train.
[All India]
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Answer:
distance=d=300km ...Given
Let the time taken to cover the distance be t and speed be x km/hr.
Speed =
time
distance
=
t
300
=x .....(1)
At increased speed,
⇒x+5=
t−2
300
...(2)
Substituting eq. (1) in eq.(2), we get
⇒
t
300
+5=
t−2
300
⇒(300+5t)(t−2)=300t
⇒300t−600+5t
2
−10t=300t
⇒5t
2
−10t−600=0
∴t
2
−2t−120=0
∴t
2
−12t+10t−120=0
∴t(t−12)+10(t−12)=0
∴(t−12)(t+10)=0
∴t=12 or t=−10
∵t cannot be negative, t=12hrs
∴ Original speed =
12
300
=25km/hr.
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