A car travels from P to Q at a constant speed. If its speed were increased by 10 km/hr, it would have taken one hour lesser to cover the distance. It would have taken further 45 minutes lesser if the speed was further increased by 10 km/hr. What is the distance between the two cities ?

A. 420 km

B. 540 km

C. 600 km

D. 650 km

Answer: Option A

Solution(By Examveda Team)

Let distance = x km and usual rate y kmph
Then,
$$\eqalign{ & \Rightarrow \frac{x}{y} - \frac{x}{{y + 10}} = 1 \cr & \Rightarrow y\left( {y + 10} \right) = 10x.....(i) \cr} $$
And,
$$\eqalign{ & \Rightarrow \frac{x}{y} - \frac{x}{{y + 20}} = \frac{7}{4} \cr & \Rightarrow y\left( {y + 20} \right) = \frac{{80x}}{7}.....(ii) \cr} $$
On dividing (i) by (ii) we get :
y = 60
Substituting y = 60 in (i), we get: x = 420 km