Two cars travel from city A to city B at a speed of 30 and 36 km/hr respectively. If one car takes 3 hours lesser time than the other car for the journey, then the distance between City A and City B is

Let the distance between City A and City B = $$d$$ km

Speed of first car = 30 km/hr and speed of second car = 36 km/hr

Let time taken by first car = $$t$$ hrs and time taken by second car = $$(t - 3)$$ hrs

Using, speed = distance/time for first car :

=> $$\frac{d}{t} = 30$$

=> $$d = 30t$$ --------------(i)

For second car, => $$\frac{d}{t - 3} = 36$$

Substituting value of $$d$$ from equation (i), we get :

=> $$30t = 36t - 108$$

=> $$36t - 30t = 6t = 108$$

=> $$t = \frac{108}{6} = 18$$ hrs

From equation (i), => $$d = 30 \times 18 = 540$$ km

=> Ans - (D)