UPSC Prelims 2022 · CSAT
Question 15: Basic Numeracy
X and Y run a 3 km race along a circular course of length 300 m. Their speeds are in the ratio 3 : 2. If they start together in the same direction, how many times would the first one pass the other (the start-off is not counted as passing)?
AnswerUPSC’s answer is (b).
Speeds are in the ratio 3 : 2. When the first runner covers the 3 km (3000 m), the second covers 2 km (2000 m), so the first gains 1000 m. He passes the other each time he gains one full lap of 300 m: 1000 ÷ 300 = 3.33, so 3 full laps are gained, giving 3 passes. The start is not counted. Relative distance divided by the lap length is the standard method.
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.
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) 2 undercounts; three laps of 300 m are gained within 1000 m.
- (b) Correct: 1000 ÷ 300 gives 3 full laps gained, so 3 passes.
- (c) 4 would need 1200 m gained, but only 1000 m is.
- (d) 5 would need 1500 m gained.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.