A car takes 15 minutes less to cover a distance of 75 km, if it increases its speed by 10 km/hr from its usual speed. How much time would it take to cover a distance of 300 km using this speed ?

A car takes 15 minutes less to cover a distance of 75 km, if it increases its speed by 10 km/hr from its usual speed. How much time would it take to cover a distance of 300 km using this speed ? Correct Answer 5 hrs

Let the usual speed be x km/hr
Then,
$$\eqalign{ & \Leftrightarrow \frac{{75}}{x} - \frac{{75}}{{x + 10}} = \frac{{15}}{{60}} \cr & \Leftrightarrow x\left( {x + 10} \right) = 3000 \cr & \Leftrightarrow {x^2} + 10x - 3000 = 0 \cr & \Leftrightarrow \left( {x + 60} \right)\left( {x - 50} \right) = 0 \cr & \Leftrightarrow x = 50 \cr} $$
∴ Required time :
$$\eqalign{ & = \left( {\frac{{300}}{{60}}} \right){\text{hrs}} \cr & = 5{\text{ hrs}} \cr} $$