In a class, 6 students can speak Tamil, 15 can speak Gujarati and 6 can speak H. If two students can speak two languages and one student can speak all the three languages, then how many students are there in the class?

• Ans:- 23
  
  Solution :-
  
  T = 6
  G = 15
  H = 6
  
  students can speak two languages (suppose Tamil & Gujarati) = 2
  student can speak all the three languages = 1
  student can speak only Tamil language = 6-2-1 = 3
  student can speak only Gujarati language = 15-2-1 = 12
  student can speak only H language = 6-1 = 5
  
  So, Total number of student = 2+1+3+12+5 = 23
• 10 years agoHelpfull: Yes(34) No(7)
• 6 tamil
  15 gujrati
  6 hindi
  let 2 people can speak gujrati and hindi
  and as given 1 speak all three
  so reduce 1 from any two
  5 tamil
  14 gujrati
  6 hindi
  
  then again reduce2 from gujrati bcoz that are counted in hindi
  so now
  5 tamil
  12 gujrati
  6 hindi
  total 23 is ans. Also asked in AMCAT
• 10 years agoHelpfull: Yes(7) No(4)
• 24 using vein diagram
• 10 years agoHelpfull: Yes(4) No(2)
• 20 is the right answer
  (6+15+6)-2*2-3*1=20
• 10 years agoHelpfull: Yes(2) No(3)
• 2 students tamil and gujrati
  2 students gujrati and hindi
  2 students himdi and tamil
  1 students can speak all
  6-(2+2+1)=1 student only tamil
  6-(2+2+1)=1 student only hindi
  15-(2+2+1)=10 student only gujrati
  so total=2+2+2+1+1+1+10=19 students
• 10 years agoHelpfull: Yes(2) No(3)
• Ans is 23
  correct ans is 23
• 10 years agoHelpfull: Yes(1) No(2)
• Tamil.....Gujrati.....Hindi
  6 15 6
  5 14 6........two students can speak both language so reduce two students either from any two language(suppose T & G)or any one language.
  
  5 14 5.........reduce one student from hindi b/c one student can speak all three languages.
  
  hence,
  ANS = 24
• 10 years agoHelpfull: Yes(0) No(2)
• 24 is correct ans using venn diagram....
• 10 years agoHelpfull: Yes(0) No(1)
• 765765 as the no would be of form abcabc
• 10 years agoHelpfull: Yes(0) No(1)
• 22
  12 spk gujrati 3 h, 3 tamil 1 speak all 3 , and 3 spks 2 lang in common
• 10 years agoHelpfull: Yes(0) No(1)
• using vein diagram, out of (15+6+6)=27 students , 1 stdnt cn spk all 3 lang and 2 cn speak any two so subtracting 27-(1+2+2+2)=20 students
• 10 years agoHelpfull: Yes(0) No(0)
• a=6,b=15,c=6 ,a intersection b=2,a intrsctn b intersection c=1
  so, aUbUc=a+b+c-2-0-0+1=6+15+6-2+1=26
• 10 years agoHelpfull: Yes(0) No(0)
• Tamil.....Gujrati.....Hindi
  6 15 6
  5 14 6........two students can speak both language so reduce two students either from any two language(suppose T & G)or any one language.
  
  5 14 5.........reduce one student from hindi b/c one student can speak all three languages.
  
  hence,
  ANS = 24
  
• 10 years agoHelpfull: Yes(0) No(0)
• from venn diagram also,
  1 student can speak all three lang. 2 student can speak two lang. suppose these 2 students know tamil & gujarati ,,,
  therefore ,ans=(6-2-1)+(15-2-1)+(6-1)+1+2=23
• 10 years agoHelpfull: Yes(0) No(0)
• 6
  15
  6
  -----------------------------1 speek all so form - 2 form any two
  menas
  6
  14
  5
  ---------------------now 2 speek two so form any 2 minus 1 1
  6
  13
  4
  
  so ans is 23................... :-)
  
• 8 years agoHelpfull: Yes(0) No(0)
• using set theory and venn diagram
  =P(A)+P(B)+P(c)-P(a and b)- p(b nd c) -P(c and a) + P(A and B and C)
  =6+15+6-2-2-2+1
  =22
• 8 years agoHelpfull: Yes(0) No(0)
• 24 is the answer
• 6 years agoHelpfull: Yes(0) No(0)