Two persons, A and B are running on a circular track. At the start, B is ahead of A and their positions make an angle of 30° at the centre of the circle. When A reaches the point diametrically opposite to his starting point, he meets B. What is the ratio of speeds of A and B, if they are running with uniform speeds?
- (a) 6 : 5 ✓ UPSC's answer
- (b) 4 : 3
- (c) 6 : 1
- (d) 4 : 2
Why the answer is (a)
• B starts 30° ahead of A. A runs half the circle (180°) to reach the point diametrically opposite its start.
• B meets A there, so B has covered 180° – 30° = 150° in the same time.
• With uniform speeds, speed ratio = distance ratio = 180 : 150 = 6 : 5, option (a).
Why the other options are wrong
- (b) 4 : 3
- 4 : 3 does not equal 180 : 150.
- (c) 6 : 1
- 6 : 1 would mean B covered only 30°.
- (d) 4 : 2
- 4 : 2 = 2 : 1 does not equal 180 : 150.
Asked in the CSAT Paper II of the UPSC Civil Services Preliminary Examination 2018, held on 3 June 2018. Question and answer key: Union Public Service Commission. Explanation: UPSC Answer Check.