UPSC Prelims 2026 · CSAT
Question 37: Basic Numeracy
X and Y are two runners who run for the same duration of time on the same circular track. They started running at the same time in the same direction with uniform speeds. When X completed 7 rounds, Y did exactly 5. After completing 5 rounds, Y changed his direction and started running in the opposite direction with speed which is double of his earlier speed. On the other hand, X continued to run with the same speed. They stopped running when X completed exactly 21 rounds. How many times did X and Y meet after they had started and before they finally stopped?
AnswerUPSC’s answer is (a).
Let X's speed be 7 and Y's 5 (rounds per unit time). In the first unit of time X completes 7 rounds and Y 5, both going the same way: X gains 2 rounds, so they meet twice, the second time at the start line as Y turns. Now they run in opposite directions at 7 and 10, closing at 17 rounds per unit time. X needs 14 more rounds to reach 21, which takes 2 units, so they cover 34 combined rounds: 34 meetings, but the last is at the instant they stop, so only 33 count. Total 2 + 33 = 35.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
This follows UPSC’s provisional key; the final key could change it.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) Right: 2 meetings in the first phase plus 33 in the second.
- (b) Wrong: 34 is the second-phase count alone, including the meeting at the final stop.
- (c) Wrong: 31 undercounts.
- (d) Wrong: 29 undercounts.
Only the provisional key (27 May 2026) was found; the final key replaces it when found.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2026, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.