UPSC Prelims 2006 · General Studies
Question 95: Basic Numeracy
There are 8 equidistant points A, B, C, D, E, F, G and H in the clockwise direction on the periphery of a circle. In a time-interval t, a person reaches from A to C with uniform motion while another person reaches the point E from the point B during the same time-interval with uniform motion. Both the persons move in the same direction along the circumference of the circle and start at the same instant. How much time after the start will the two persons meet each other?
AnswerThe answer is (b).
Number the points A to H as 0 to 7 around the circle. In time t the first person goes from A (0) to C (2), two steps; the second goes from B (1) to E (4), three steps. After x units of time, the first is at 2x and the second at 1 + 3x (mod 8). They meet when 2x = 1 + 3x (mod 8), so x = -1 (mod 8), and the smallest positive value is x = 7. So they meet after 7t.
Why each option is right or wrong
- (a) At 4t they are at 0 and 5 (mod 8); not together.
- (b) Correct: x = 7 gives both at point 6 (mod 8).
- (c) At 9t they are at 2 and 4 (mod 8); not together.
- (d) They do meet, at 7t.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2006, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.