question_answer

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 = 5