A bus covers a distance of 240 km at a uniform speed. Due to heavy rain its speed gets reduced by 10 km/h and as such it takes two hours longer to cover the total distance. Assuming the uniform speed to be 'x' km/h, form an equation and solve it to evaluate x.

Uniform speed of bus = x km/h

Due to heavy rain the speed reduces to = (x - 10) km/h

Given, due to decrease in speed it takes two hours longer to cover the distance

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

$\therefore \dfrac{240}{x - 10} - \dfrac{240}{x} = 2 \\[1em] \Rightarrow \dfrac{240x - 240(x - 10)}{x(x - 10)} = 2 \text{ (On taking L.C.M.) } \\[1em] \Rightarrow 240x - 240x + 2400 = 2x(x - 10) \\[1em] \Rightarrow 2400 = 2x^2 - 20x \\[1em] \Rightarrow 2x^2 - 20x - 2400 = 0 \\[1em] \Rightarrow 2(x^2 - 10x - 1200) = 0 \\[1em] \Rightarrow x^2 - 10x - 1200 = 0 \\[1em] \Rightarrow x^2 - 40x + 30x - 1200 = 0 \\[1em] \Rightarrow x(x - 40) + 30(x - 40) = 0 \\[1em] \Rightarrow (x + 30)(x - 40) = 0 \\[1em] \Rightarrow x + 30 = 0 \text{ or } x - 40 = 0 \\[1em] x = -30 \text{ or } x = 40$

Since, speed cannot be negative hence, x ≠ -30.

The equation in x is $\rightarrow \dfrac{240}{x - 10} - \dfrac{240}{x} = 2$
Hence, the value of uniform speed is 40 km/h.