188
In above Venn diagram the letters label regions identified as follows:
All the numbers are percentages.
A Non-readers (8)
B Read newspaper A only
C Read newspaper B only
D Read newspaper C only
E Read A and C only
F Read B and C only
G Read A and B only
H Read all three newspapers
A+B+C+D+E+F+G+H=100 (all the people)
B+C+D+E+F+G+H=100-8=92
B+E+G+H=42 (A readers);
C+F+G+H=51 (B readers)
D+E+F+H=68 (C readers)
We have to interpret the statement: 36% read A and C. This could mean they (a) Read A and C only or (b) Read A and C and possibly B. Similarly with the 28% reading B and C and the 30% reading A and B.
If we look at (a) first, this implies that E+G=30+36=66; but E+G+B+H=42, so B+H=-24, which cannot be since all the percentages have to be positive. So interpretation (b) is the acceptable one. This means that:
(E+H)+(G+H)=E+G+2H=30+36=66 and E+G=66-2H, so:
E+G+B+H=42=66-2H+B+H=66+B-H.
Therefore H-B=24 or B=H-24. Now we have B and E+G in terms of H.
Similarly, (E+H)+(F+H)=E+F+2H=36+28=64 and E+F=64-2H, so:
E+F+D+H=68=64-2H+D+H=64+D-H.
Therefore 4=D-H or D=H+4.
And (F+H)+(G+H)=F+G+2H=58 and F+G=58-2H, so:
F+G+C+H=51=58-2H+C+H=58+C-H.
Therefore H-C=7 or C=H-7.
Substituting for the variables that we have in terms of H, we can write:
(E+G)+(E+F)+(F+G)=66-2H+64-2H+58-2H=188-6H=2(E+F+G); E+F+G=94-3H.
B+C+D=H-24+H-7+H+4=3H-27 so B+C+D+E+F+G+H=3H-27+94-3H+H=92.
H=92-94+27=25, so 25% of the people read all three newspapers.