In a group of persons travelling in a bus, 6 persons can speak Tamil, 15 can speak Hindi and 6 can speak Gujarati. In that group, none can speak any other language. If 2 persons in the group can speak two languages and one person can speak all the three languages, then how many persons are there in the group?

A) 21 B) 23 C) 22 D)24

• Let us assume the two persons who can speak two languages speak Hindi and Tamil. The third person then speaks all the three languages.
  
  Tamil – Number of persons who can speak is 6. Only Tamil 6 – 2 – 1 = 3
  
  Hindi - Number of persons who can speak is 15. Only Hindi 15 – 2 – 1 12
  
  Gujarati – Number of persons who can speak is 6. Only Gujarati 6 – 1 = 5
  
  Thus the number of persons who can speak only one language is 3 + 12 + 5 = 20
  
  Number of persons who can speak two languages = 2
  
  Number of person who an speak all the languages = 1
  
  Total number of persons = 23.
• 10 years agoHelpfull: Yes(34) No(1)
• 23
  
  Let two person can speak tamil and hindi, then we say:
  Tamil 6 -2=4
  Hindi 15-0=15
  Guj 6-0=6
  
  The two persons who can speak the first two language shall only be counted in one group and subtracted from the other group.
  
  If one person can speak all the three languages, he/she shall only be counted in one group and deducted from two groups:
  Tamil 6 -2=4- 0= 4
  Hindi 15-0=15-1=14
  Guj 6-0 =6- 1= 5
  Total is 23
• 13 years agoHelpfull: Yes(28) No(5)
• Let T, H, G be Tamil, Hindi, Gujarati respectively.
  From the given, T=6 H=15 G=6
  Any 2 languages=2 All three languages = 3
  
  
  possibility 1:
  
  two speak T and H
  
  only T= 6-2-1=3
  only H=15-2-1=12
  only G=6-1=5
  
  Total no of people speaks only one lang is = 20
  Total no of persons = ( no of persons speaks only one )+( no of prsns speaks two lang)+(no of persons speaks three)
  
  = 20 + 2 + 1 = 23
  
  
  possibility 2:
  
  
  two speak T and G
  
  only T=3
  only H=14
  only G= 3
  
  total only= 20
  
  total persons = 20 + 2+ 1= 23
  
  
  possibility :3
  
  two speaks H and G
  
  only T=5
  only H=12
  only G=3
  
  total only=20
  
  total persons = 20 + 2+1= 23
  
  
  
  so the ans is 23
• 8 years agoHelpfull: Yes(5) No(1)
• n(T) = 6; n(H) = 15; n(G) = 6
  
  n(T ∩ H ∩ G) = 1
  
  n(T ∩ H) = n(H ∩ G) = n(T ∩ G) = 2
  
  n(T U H U G) = n(T) + n(H) + n(G) - n(T ∩ H) - n(H ∩ G) - n(T ∩ G) + n(T ∩ H ∩ G)
  
  = 6 + 15 + 6 - 2 - 2 - 2 + 1 = 22
  
  The correct option is B.
• 6 years agoHelpfull: Yes(2) No(1)
• Ans: D) 24
  
  
  Let T, H, G be Tamil, Hindi, Gujarati respectively.
  From the given, T=6 H=15 G=6
  Any 2 languages=2 All three languages = 3
  
  (i) First possibility:
  Let the two languages be T and H
  Then, Only T=4 H=13 G=5
  Hence the number of persons in the group =4+13+5+1+1 =24
  (ii) Second possibility:
  Let the two languages be T and G
  Then, Only T=4 H=14 G=4
  Hence the number of persons in the group =4+14+4+1+1 =24
  (iii) First possibility:
  Let the two languages be G and H
  Then, Only T=5 H=13 G=4
  Hence the number of persons in the group =5+13+4+1+1 =24
  
  
  
• 9 years agoHelpfull: Yes(1) No(7)
• Tamil – Number of persons who can speak is 6. Only Tamil 6 – 2 – 1 = 3
  
  Hindi - Number of persons who can speak is 15. Only Hindi 15 – 2 – 1 12
  
  Gujarati – Number of persons who can speak is 6. Only Gujarati 6 – 1 = 5
  
  Thus the number of persons who can speak only one language is 3 + 12 + 5 = 20
  
  Number of persons who can speak two languages = 2
  
  Number of person who an speak all the languages = 1
  
  Total number of persons = 23
• 5 years agoHelpfull: Yes(1) No(0)
• 6+15+6-(2+1*2)
• 10 years agoHelpfull: Yes(0) No(1)
• how can we assume that the two languages will be only tamil and hindi?
  it could also possible :tamil and hindi , hindi and gujarati , gujarati and tamil
• 6 years agoHelpfull: Yes(0) No(0)