Correct Answer - Option 1 : 5,000
Given:
Three-tenth of total voters promised to vote for A and the rest promised to vote for B.
On the last day of the election, 20% of voters went back of their promise to vote for A and 25% of voters went back of their promise to vote for B.
A lost the election by 850 votes.
Calculation:
Let the total number of voters be x.
Three-tenth of total voters promised to vote for A and the rest promised to vote for B.
Voters who promised to vote for A = 3x/10
Total voters = Voters who promised to vote for A + Voters who promised to vote for B
⇒ x = 3x/10 + Voters who promised to vote for B
⇒ Voters who promised to vote for B = x – 3x/10 = 7x/10
On the last day of the election, 20% of voters went back of their promise to vote for A and 25% of voters went back of their promise to vote for B.
Number of voters who backed out for A = 20% of 3x/10 = 3x/50
Number of voters who backed out for B = 25% of 7x/10 = 7x/40
Number of votes obtained by A = Voters who promised to vote for A + Number of voters who backed out for B - Number of voters who backed out for A
⇒ 3x/10 + 7x/40 – 3x/50 = 83x/200
Number of votes obtained by B = Voters who promised to vote for B + Number of voters who backed out for A - Number of voters who backed out for B
⇒ 7x/10 + 3x/50 – 7x/40 = 117x/200
A lost the election by 850 votes.
⇒ (117x/200) – (83x/200) = 850
⇒ 34x/200 = 850
⇒ x = 850 × 200/34
⇒ x = 5,000
∴ Total number of voters were equal to 5,000.
