UPSC Prelims 2026 · CSAT Paper 2 · Set DMathematicsQ 17 / 80

UPSC Prelims 2026 CSAT Paper 2 — Question 17

Question

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?

(a)35
(b)34
(c)31
(d)29

UnlockIAS answer: (a)35

Solution

Speeds are in ratio 7 : 5. Until Y finishes 5 rounds (when X has done 7) the same-direction gap of 2 rounds gives meetings; thereafter Y reverses at double speed while X runs to 21 rounds. Counting the relative laps and excluding the start and final-stop instants gives 35 meetings.

UnlockIAS expert key, prepared 24 May 2026 and cross-verified by re-deriving the answer — this is our key, not the official UPSC provisional key (awaited).

Section

Mathematics

Topic Reference

Numeracy — Circular motion / races

Official UPSC key still awaited

UPSC has announced (PIB Release 2262441, 18 May 2026) that the provisional answer key for CSE Prelims 2026 will be released “soon after Exam”. Until then, use the CSAT score calculator for your qualifying-status estimate, and join the per-question discussion below.

CSAT Score Calculator

Check your 33% qualifying status

Official Notification

PIB Release 2262441

Back to all 80 CSAT questions