Two cars travel from city A to city B at a speed of 24 and 32 km/hr respectively. If one car takes 2.5 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 = 24 km/hr and speed of second car = 32 km/hr

Let time taken by first car = $$t$$ hrs and time taken by second car = $$(t - 2.5)$$ hrs

Using, speed = distance/time for first car :

=> $$\frac{d}{t} = 24$$

=> $$d = 24t$$ --------------(i)

For second car, => $$\frac{d}{t - 2.5} = 32$$

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

=> $$24t = 32t - 80$$

=> $$32t - 24t = 8t = 80$$

=> $$t = \frac{80}{8} = 10$$ hrs

From equation (i), => $$d = 24 \times 10 = 240$$ km

=> Ans - (C)