Question: A train travels a distance of 300 km at a constant speed. If the speed of the train is increased by 5 km/h the journey would have taken 2 h less. The original speed of the train was
Options:
A) 25 km/h
B) 20 km/h
C) 28 km/h
D) 30 km/h
Show Answer
Answer:
Correct Answer: A
Solution:
- Let the normal speed of train be x km/h.
Let the normal time of train = T h
$ \therefore $ $ Time=\frac{Distance}{Speed} $
So $ \frac{300}{x}=T $
(i)
Similarly, $ \frac{300}{x+5}=T-2 $ … (ii)
On solving Eqs. (i) and (ii), we get
$ \frac{300}{x+5}=\frac{300}{x}-2 $
$ \Rightarrow $ $ \frac{300}{x+5}=\frac{300-2x}{x} $
$ \Rightarrow $ $ 300x=(x+5)(300-2x) $
$ \Rightarrow $ $ 300x=300x-2x^{2}+1500-10x $
$ \Rightarrow $ $ -2x^{2}+1500-10x=0 $
$ \Rightarrow $ $ x^{2}-750+5x=0 $
$ \Rightarrow $ $ x^{2}+5x-750=0 $
$ \Rightarrow $ $ x^{2}+30x-25x-750=0 $
$ \Rightarrow $ $ x(x+30)-25(x+30)=0 $
$ \therefore $ $ x=25, $ $ -30 $
Since, speed of train cannot be negative, hence speed of train is 25 km/h,
BETA
