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: Option (b) implies a meeting time of 2 hours and 20 minutes, which would require a relative speed of approximately 66.67 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: Option (d) implies a meeting time of 3 hours and 10 minutes, which would require a relative speed of approximately 50.32 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.