Question

In an election involving three parties for the chairmanship election of Ogun State, voters cast their votes as follows: 

190 votes for party A, 200 for party B and 250 for party C, 80 votes for A and B, 60 votes for A and C, 100 votes for B and C, and 40 votes for B alone. If 500 people voted during the election, find

a.) The number of voters who voted for all the three parties

b.) The number of voters who voted for A and B but not C

c.) The number of voters who did not vote for any party

Answer 1

Let d people who voted 4 d three parties = x

B only = 200-(100 - x + 80 - x + x) = 40

x = 20(20 people voted 4 d 3 parties)

A only = 190-(60 - x + 80 - x + x) since x = 20, A only = 70 people

Conly = 250-(60 - 20 + 100 - 20 + 20) = 110 people

B only = 40 (given)

No of people who did not vote = y

Therefore, 

70 + 40 + 110 + 60 + 40 + 80 + 20 + y = 500

y = 80 people...

(a) no of people who voted all d parties = 20

(b) no of people who voted for A and B but not C = 60

(c) no of people who did not vote = 80