A bus and a car start from points x and y respectively and travel towards each other at the speed of 60 km/h and 50 km/h respectively. By the time they meet, the bus has travelled 50 km more than the car. What is the distance between x and y?

Correct option is D

Given:
Speed of the bus $$v_b$$​  = 60 km/h
Speed of the car $$v_c$$​  = 50 km/h
By the time they meet, the bus has traveled 50 km more than the car.
Let, Distance traveled by the car when they meet = d km
Distance traveled by the bus when they meet = d + 50 km
Concept Used:
Time taken by the bus $$t_b = \frac{d + 50}{60}$$​
Time taken by the car $$t_c = \frac{d}{50}$$​
​$$t_b = t_c$$​

Solution:​

Now,

​$$\frac{d + 50}{60} = \frac{d}{50}$$​

50(d + 50) = 60d

2500 = 60d - 50d

2500 = 10d

​$$d = \frac{2500}{10} = 250 \text{ km}$$​

d + 50 = 250 + 50 = 300 km

Total distance = Distance traveled by bus + Distance traveled by car

Total distance = 300 + 250 = 550 km

Option (D) is right.