Two cars start towards each other, from two places A and B which are at a distance of 160 km. They start at the same time 08 : 10 AM. If the speeds of the cars are 50 km and 30 km per hour respectively, they will meet each other at
- (a) 10 : 10 AM ✓ UPSC's answer
- (b) 10 : 30 AM
- (c) 11 : 10 AM
- (d) 11 : 20 AM
Why the answer is (a)
• The total distance between the two cars is 160 km.
• Since they are moving towards each other, their relative speed is the sum of their individual speeds: 50 km/h + 30 km/h = 80 km/h.
• The time taken to meet is calculated by dividing the total distance by the relative speed: 160 km / 80 km/h = 2 hours.
• The cars start at 08:10 AM.
• Adding 2 hours to the start time gives 10:10 AM.
• Therefore, the cars will meet at 10:10 AM, which corresponds to option (a).
Why the other options are wrong
- (b) 10 : 30 AM
- 10:30 AM is 2 hours 20 minutes after the start, which would need a relative speed of about 68.57 km/h, not 80 km/h.
- (c) 11 : 10 AM
- Option (c) implies a meeting time of 3 hours, which would require a relative speed of approximately 53.33 km/h, not 80 km/h.
- (d) 11 : 20 AM
- 11:20 AM is 3 hours 10 minutes after the start, which would need a relative speed of about 50.53 km/h, not 80 km/h.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2014, held on 24 August 2014. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.