A publishing firm publishes newspapers 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% |
Newspapers C is read by 14% |
Newspapers A and B are read by 11% |
Newspapers B and C are read by 10% |
Newspapers C and A are read by 9% |
Newspaper C only is read by 0% |
The percentage of readers who read all the three newspapers is |
A) 1
B) 4
C) 5
D) 6
Correct Answer: C
Solution :
Let the number of persons be 100. Then, we have \[P+Q+S+T=26\] ? (i) \[Q+R+T+U=25\] ? (ii) \[S+T+U+V=14\] ... (iii) \[Q+T=11\] ... (iv) \[T+U=10\] ... (v) \[S+T=9\] ... (vi) \[V=0\] ... (vii) Putting V = 0 in Eq. (in), we get \[S+T+U=14\] But \[T+U=10\] So, \[S=(14-10)=4\] From Eq. (vi), we have \[T=9-S=9-4=5\] From Eq. (v), we have \[U=10-T=5\] From Eq. (iv), we have \[Q=11-T=6\] From Eq. (i), we have \[P=26-(Q+S+T)=26-(6+4+5)=11\] From Eq. (ii), we have \[R=25-(Q+T+U)=25-(6+5+5)=9\] So, percentage of readers who read all the newspapers = T = 5You need to login to perform this action.
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