Read the following information carefully to answer the questions that follow :
A sample poll of 200 votes revealed the following information concerning three candidates A, B and C of a certain party who were running for three different offices. 28 in favour of both A and B. 98 in favour of A or B but not C. 42 in favour of B but not A or C. 122 in favour of of B or C but not A. 64 in favour of C but not A or B. 14 in favour of A and C but not B.
Q. No. 1:
How many votes were in favour of all the three candidates ?
Here, g+d = 28......(i) a+d+b = 98 .......(ii) b = 42 .......(iii) b+c+e = 122 ......(iv) c = 64 ............(v) f = 14 ..........(vi) a+b+c+d+e+f+g = 200 .......(vii) Thus from all equations, a = 36, b = 42, c= 64, d= 20, e = 16, f = 14, g = 8. Clearly 8 votes were in favour of all the three candidates.
Q. No. 2:
How many votes were in favour of A irrespective of B or C ?
Here, g+d =
28......(i) a+d+b = 98 .......(ii) b = 42
.......(iii) b+c+e = 122 ......(iv) c = 64
............(v) f = 14 ..........(vi) a+b+c+d+e+f+g =
200 .......(vii) Thus from all equations, a = 36, b =
42, c= 64, d= 20, e = 16, f = 14, g = 8. Number of votes favouring A irrespective of B or C = 36+20 + 8+ 14 = 78
Q. No. 3:
How many votes were in favour of B irrespective of A or C?
Here, g+d =
28......(i) a+d+b = 98 .......(ii) b = 42
.......(iii) b+c+e = 122 ......(iv) c = 64
............(v) f = 14 ..........(vi) a+b+c+d+e+f+g =
200 .......(vii) Thus from all equations, a = 36, b =
42, c= 64, d= 20, e = 16, f = 14, g = 8. No. of votes favouring B irrespective of A or C = 42+20+16+8 = 86.
Q. No. 4:
How many votes were in favour of C irrespective of A or B ?
Here, g+d =
28......(i) a+d+b = 98 .......(ii) b = 42
.......(iii) b+c+e = 122 ......(iv) c = 64
............(v) f = 14 ..........(vi) a+b+c+d+e+f+g =
200 .......(vii) Thus from all equations, a = 36, b =
42, c= 64, d= 20, e = 16, f = 14, g = 8. No. of votes favouring C irrespective of B or C = 64+14+8+16 = 102.
Q. No. 5:
How many votes were in favour of A and B but not C ?
Here, g+d =
28......(i) a+d+b = 98 .......(ii) b = 42
.......(iii) b+c+e = 122 ......(iv) c = 64
............(v) f = 14 ..........(vi) a+b+c+d+e+f+g =
200 .......(vii) Thus from all equations, a = 36, b =
42, c= 64, d= 20, e = 16, f = 14, g = 8. The total number of voters favouring only one of the candidates => a+b+c = 36+42+64 = 142.
Q. No. 7:
How many votes were in favour of A and C but not B ?
Here, g+d =
28......(i) a+d+b = 98 .......(ii) b = 42
.......(iii) b+c+e = 122 ......(iv) c = 64
............(v) f = 14 ..........(vi) a+b+c+d+e+f+g =
200 .......(vii) Thus from all equations, a = 36, b =
42, c= 64, d= 20, e = 16, f = 14, g = 8. Number of votes favouring A and C but not B = f = 14.
Q. No. 8:
How many votes were in favour of B and C but not A?
Here, g+d =
28......(i) a+d+b = 98 .......(ii) b = 42
.......(iii) b+c+e = 122 ......(iv) c = 64
............(v) f = 14 ..........(vi) a+b+c+d+e+f+g =
200 .......(vii) Thus from all equations, a = 36, b =
42, c= 64, d= 20, e = 16, f = 14, g = 8. Number of votes favouring B and C but not A = e =16.
Q. No. 14:
Which is the most suitable diagram among the following, which represents interrelationship among anti social elements(A), Pickpockets (P) and Blackmailers(B) ?