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 Mathematics
17 failed in both Mathematics and English
5 failed in all three tests
Concept used :

Venn diagram concept
Calculations: Candidates failed in atleast one subject
⇒ Candidates failed in one subject + candidates failed on two subject + candidates failed in three subject
Candidates failed in english =30
Candidates failed in Hindi =75
Candidates failed in mathematics =50
Candidates failed in english and hindi only =10
Candidates failed in english and mathematics only =12
Candidates failed in Hindi and mathematics only =12
Candidates failed in Hindi, english and mathematics =5
Candidates failed in atleast one subject =30+75+50+10+12+12+5
⇒194
Percentage of candidates failed in atleast one subject
⇒ (Candidates failed in atleast one subject/Total candidates )×100
⇒(194∕500)
⇒38.8%
∴ Percentage of candidates failed in atleast one subject is 38.8%