UPSC Prelims 2016 · CSAT
Question 75: Basic Numeracy
A and B walk around a circular park. They start at 8 a.m. from the same point in the opposite directions. A and B walk at a speed of 2 rounds per hour and 3 rounds per hour respectively. How many times shall they cross each other after 8.00 a.m. and before 9.30. a.m. ?
AnswerUPSC’s answer is (a).
They walk in opposite directions, so they approach each other at the sum of their speeds: 2 + 3 = 5 rounds an hour. In 1.5 hours the combined distance is 7.5 rounds, and they cross once for each full round of combined distance, at 1, 2, ... 7 rounds. So 7 crossings. The leftover half round does not make another crossing.
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) Right: crossings occur at 1 to 7 combined rounds.
- (b) 6 misses the seventh crossing before 9.30.
- (c) 5 undercounts the crossings.
- (d) 8 would need 8 combined rounds, but only 7.5 are covered.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2016, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.