Question

Two cars A and B started from the same place and at the same time and in the same direction at speeds of 45 km/h and 75 km/h. B reaches the destination 300 km away and turned back towards the starting point. While returning B crosses A. Find the distance from the start point where both cars crossed each other?
1. 210 km
2. 230 km
3. 220 km
4. 225 km

Answer 1

Correct Answer - Option 4 : 225 km

Given:

Speed of car A = 45 km/h

Speed of car B = 75 km/h

Distance between the initial and final point = 300 km

Concept:

Calculate the time in which B reached the destination. A will cover some distance in that time, and after that their speed will add up to give the relative speed and both the cars would meet after that point.

Formula used:

Speed = Distance/Time

Calculation:

Time taken by car B to travel 300 km = (300/75) hr

= 4 hr

Distance traveled by car A in 4 hrs = (45 × 4) km

= 180 km

∴ The two cars will cross after 180 km.

Distance left to be traveled by car A = (300 - 180) km

= 120 km

∵ After 180 km, both the cars will travel in the opposite directions with respect to each other.

∴ Relative speed of car A w.r.t to car B = (45 + 75) km/h

= 120 km/h

∴ Time after which both the cars will meet = (120/120) hr

= 1 hr

∴ Distance traveled by car A in 1 hr = ( 45 × 1) km

= 45 km

∴ Distance from the starting point after which both the cars will cross each other = (180 + 45) km

= 225 km