If the speed of a car is increased by 10 km per hour, it takes 18 minutes less to cover a distance of 36 km. Find the speed of the car.

Let speed be x km/hr.

Time taken to cover 36 km = $\dfrac{36}{x}$ hr

Increasing speed by 10 km/hr we get speed = (x + 10) km/hr

Time taken to cover 36 km = $\dfrac{36}{x + 10}$ hr

According to question,

$\Rightarrow \dfrac{36}{x} - \dfrac{36}{x + 10} = \dfrac{18}{60} \\[1em] \Rightarrow \dfrac{36(x + 10) - 36x}{x(x + 10)} = \dfrac{18}{60} \\[1em] \Rightarrow \dfrac{36x - 36x + 360}{x^2 + 10x} = \dfrac{3}{10} \\[1em] \Rightarrow \dfrac{360}{x^2 + 10x} = \dfrac{3}{10} \\[1em] \Rightarrow 3600 = 3(x^2 + 10x) \\[1em] \Rightarrow 1200 = x^2 + 10x \\[1em] \Rightarrow x^2 + 10x - 1200 = 0 \\[1em] \Rightarrow x^2 + 40x - 30x - 1200 = 0 \\[1em] \Rightarrow x(x + 40) - 30(x + 40) = 0 \\[1em] \Rightarrow (x - 30)(x + 40) = 0 \\[1em] \Rightarrow x - 30 = 0 \text{ or } x + 40 = 0 \\[1em] \Rightarrow x = 30 \text{ or } x = -40.$

Since, speed cannot be negative

∴ x = 30 and x + 10 = 40.

Hence, speed of car = 30 km/hr.