The speed of an ordinary train is x km per hour and that of an express train is (x + 25) km per hr.

(i) Find the time taken by each train to cover 300 km.

(ii) If the ordinary train takes 2 hrs more than the express train; calculate the speed of the express train.

(i) We know that,

Time = $\dfrac{\text{Distance}}{\text{Speed}}$

Time taken by ordinary train = $\dfrac{300}{x}$

Time taken by express train = $\dfrac{300}{x + 25}$

Hence, time taken by ordinary train = $\dfrac{300}{x}$ hours and $\dfrac{300}{x + 25}$ hours.

(ii) According to question,

$\Rightarrow \dfrac{300}{x} - \dfrac{300}{x + 25} = 2 \\[1em] \Rightarrow \dfrac{300(x + 25) - 300x}{x(x + 25)} = 2 \\[1em] \Rightarrow \dfrac{300x + 7500 - 300x}{x^2 + 25x} = 2 \\[1em] \Rightarrow \dfrac{7500}{x^2 + 25x} = 2 \\[1em] \Rightarrow 7500 = 2(x^2 + 25x) \\[1em] \Rightarrow 2x^2 + 50x - 7500 = 0 \\[1em] \Rightarrow 2(x^2 + 25x - 3750) = 0 \\[1em] \Rightarrow x^2 + 25x - 3750 = 0 \\[1em] \Rightarrow x^2 + 75x - 50x - 3750 = 0 \\[1em] \Rightarrow x(x + 75) - 50(x + 75) = 0 \\[1em] \Rightarrow (x - 50)(x + 75) = 0 \\[1em] \Rightarrow x - 50 = 0 \text{ or } x + 75 = 0 \\[1em] \Rightarrow x = 50 \text{ or } x = -75.$

Since, speed cannot be negative

∴ x = 50 and x + 25 = 75.

Hence, speed of express train = 75 km/hr.