UPSC Prelims 2000 · General Studies
Question 141: Basic Numeracy
In an examination, every candidate took Physics or Mathematics or both. 65.8% took Physics and 59.2% took Mathematics. The total number of candidates was 2000. How many candidates took both Physics and Mathematics?
AnswerThe answer is (b).
Everyone took Physics or Mathematics or both, so the two percentages add up to more than 100 only because of those who took both. Both = 65.8 + 59.2 - 100 = 25 per cent. Of 2,000 candidates, 25 per cent is 500. This is the inclusion-exclusion rule: Physics + Mathematics - Both = all candidates.
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 an unofficial answer: UPSC has not published its key for this year, and if that answer is wrong, so is this path.
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) 750 would be 37.5 per cent, which does not match.
- (b) Right: 25 per cent of 2,000 = 500.
- (c) 250 would be 12.5 per cent, which does not match.
- (d) 125 would be 6.25 per cent, which does not match.
Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2000, General Studies. UPSC's own paper isn't online; the words are from a published compilation. The paper on upsc.gov.in.