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Three-tenth of total voters promised to vote for A and the rest promised to vote for B. On last day of 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 due to which A lost the election by 850 votes. Total number of voters were equal to - 
1. 5,000
2. 4,000
3. 3,400
4. 6,800

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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.

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