mathematics
posted by partey .
1. In an examination conducted for 80 candidates, those who passed in mathematics were 17 more than those who passed science and 9 failed both subjects.14 candidates passed both subjects. I. Draw a venn diagram to illustrate this information II. How many students passed in mathematics? III. How many students passed in science? IV. How many passed exactly one subject?

I assume you can draw the Venn diagram. The universe is 80, the population outside the circles is 9, the population of the intersection of the circles is 14.
If you add M+S, you count twice the 14 who passed both.
so, M + S  14 = 809 = 71
M + S = 85
M = 17+S
2S + 17 = 85
2S = 68
S = 34
so, M = 51 
23,34