Find How Many Watch All Three Games Find How Many Watch All Three Games Question: A survey of 500 television viewers produced the following information: 285 watch football, 195 watch hockey, 115 watch basketball, 45 watch football and basketball, 70 watch football and hockey, 50 watch hockey and basketball, 50 do not watch any of […]

Find Hindi Only, Bengali Only and Both Speakers Find Hindi Only, Bengali Only and Both Speakers Question: In a group of 1000 people, there are 750 who can speak Hindi and 400 who can speak Bengali. How many can speak Hindi only? How many can speak Bengali only? How many can speak both Hindi and

Find Total Members in Three Athletic Teams Find Total Members in Three Athletic Teams Question: Of the members of three athletic teams in a certain school, 21 are in the basketball team, 26 in hockey team and 29 in the football team. 14 play hockey and basketball, 15 play hockey and football, 12 play football

Find People Who Read Newspapers H, T and I Find People Who Read Newspapers H, T and I Question: In a survey of 60 people, it was found that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T, 8

Find How Many Drink Tea and Coffee Find How Many Drink Tea and Coffee Question: In a group of 50 persons, 14 drink tea but not coffee and 30 drink tea. Find: (i) how many drink tea and coffee both (ii) how many drink coffee but not tea. Solution (i) \[ n(T)=n(T-C)+n(T\cap C) \] \[

Find How Many Speak Hindi and English Find How Many Speak Hindi and English Question: In a group of 950 persons, 750 can speak Hindi and 460 can speak English. Find: (i) how many can speak both Hindi and English (ii) how many can speak Hindi only (iii) how many can speak English only Solution

Find Percentage of Indians Who Like Both Orange and Bananas Find Percentage of Indians Who Like Both Orange and Bananas Question: A survey shows that 76% of the Indians like orange, whereas 62% like bananas. What percentage of the Indians like both orange and bananas? Solution \[ n(O\cup B)=n(O)+n(B)-n(O\cap B) \] Since every Indian likes

Find n(B), n(A−B) and n(B−A) Find n(B), n(A−B) and n(B−A) Question: Let \( A \) and \( B \) be two sets such that: \[ n(A)=20,\quad n(A\cup B)=42,\quad n(A\cap B)=4 \] Find: \[ (i)\ n(B) \] \[ (ii)\ n(A-B) \] \[ (iii)\ n(B-A) \] Solution (i) Find \( n(B) \) \[ n(A\cup B)=n(A)+n(B)-n(A\cap B) \]

Find How Many Like Both Coffee and Tea Find How Many Like Both Coffee and Tea Question: In a group of 70 people, 37 like coffee, 52 like tea and each person likes at least one of the two drinks. How many like both coffee and tea? Solution \[ n(C\cup T)=n(C)+n(T)-n(C\cap T) \] \[ 70=37+52-n(C\cap

Find How Many Teachers Teach Physics Find How Many Teachers Teach Physics Question: In a school there are 20 teachers who teach mathematics or physics. Of these, 12 teach mathematics and 4 teach physics and mathematics. How many teach physics? Solution \[ n(M\cup P)=n(M)+n(P)-n(M\cap P) \] \[ 20=12+n(P)-4 \] \[ 20=8+n(P) \] \[ n(P)=20-8 \]