A publishing firm publishes newspaper A, B and C. In an effort to persuade advertisers to insert advertisements in these newspapers, the firm sends out the following statement to possible advertisers :
A survey of representative sample of the whole population shows that Newspaper A is read by 26%, |Newspaper B is read by 25%, Newspaper C is read by 14%, Newspaper A and B are read by 11%, Newspaper B and C are read by 10%, Newspaper C and A are read by 9%, Newspaper C only is read by 0%.
The percentage of readers who read A and B but not C, is

Options

A. 2
B. 4
C. 5
D. 6

Answer

D

Explanation

`a + b + d +e = 26 " " ...(i)`
`b + c + e + f = 25" "... (ii) `
`d + e + f + g = 14 " " ... (iii) `
`b + e= 11 " " ... (iv) `
`e + f = 10 " " ... (v) `
`d + e = 9 " " ... (vi)`
`g = 0 " " ... (vii) `
Putting g = 0 from (vii) in (iii), we get `d +e+f+0= 14 `
or, `9+f=14 " " [because d + e = 9," from (vi)"]`
or `f = 14-9=5 " " ... (viii) `
Putting f=5 from (viii) in (v), we get e +5 = 10
or, `e=5 " " .... (ix)`
Putting e = 5 from (ix) in (iv), we get `b + 5 = 11 `
or, `b = 6 " "... (x) `
Putting e =5 from (ix) in (vi), we get `d + 5 = 9 `
or, `d=4 " " .... (x i) `
Putting b = 6, e=5, f=5 in (ii), we get 6+c+5+5 = 25
or, `c=9 " " ... (x ii) `
Putting b = 6, d= 4, e=5 in (i), we get a +6+4 +5 = 26
or `a = 11 `Therefore, Required percentage of readers who read newspaper A and B but not C= b = 6