UPSC CDS 1 2022 Math Paper

Given :
Total candidates appeared in an examination =500
30 candidates failed in English only
75 failed in Hindi only
50 failed in mathematics only and
15 failed in both English and Hindi
17 failed in both Hindi and Mathematics1 17 failed in both Mathematics and English
5 failed in all three tests
Concept used :
Venn diagram concept Calculations: Candidates failed in at least 2 subjects = candidates failed in 2 subjects + candidates failed in 3 subjects
Candidates failed in only English and mathematics =12
Candidates failed in only English and Hindi =10
Candidates failed in only Hindi and mathematics =12
Candidates failed in Hindi, English, and mathematics =5
Candidates failed in at least 2 subjects =12+10+12+5=39
Percentage of candidates who failed in at least two subjects
⇒ (candidates failed in at least 2 subjects/total candidates )×100
⇒(39∕500)×100=39∕5
⇒7.8%
∴ The percentage of candidates who failed in at least two subjects is 7.8% .