Login/Sign Up
Home » A passenger train takes 2 hours less for a journey of if its speed is increased by from its usual speed. Find its usual speed.
A passenger train takes 2 hours less for a journey of 300 \mathrm{~km} if its speed is increased by 5 \mathrm{~km} / \mathrm{hr} from its usual speed. Find its usual speed.
CBSE | Class 10 | Exercise 10e | Maths | Quadratic Equations | RS Aggarwal
A passenger train takes 2 hours less for a journey of 300 \mathrm{~km} if its speed is increased by 5 \mathrm{~km} / \mathrm{hr} from its usual speed. Find its usual speed.

Let the usual speed x \mathrm{~km} / \mathrm{hr}.

According to the question:

\begin{array}{l} \frac{300}{x}-\frac{300}{(x+5)}=2 \\ \Rightarrow \frac{300(x+5)-300 x}{x(x+5)}=2 \\ \Rightarrow \frac{300 x+1500-300 x}{x^{2}+5 x}=2 \\ \Rightarrow 1500=2\left(x^{2}+5 x\right) \\ \Rightarrow 1500=2 x^{2}+10 x \\ \Rightarrow x^{2}+5 x-750=0 \\ \Rightarrow x^{2}+(30-25) x-750=0 \\ \Rightarrow x^{2}+30 x-25 x-750=0 \\ \Rightarrow x(x+30)-25(x+30)=0 \\ \Rightarrow(x+30)(x-25)=0 \\ \Rightarrow x=-30 \text { or } x=25 \end{array}

The usual speed cannot be negative; therefore, the speed is 25 \mathrm{~km} / \mathrm{hr}.

i

More Material