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In the previous election, 150000 voted for a constituency where only two candidates A and B contested. Due to awareness campaign, 20% more people voted this time. Assuming all people who voted earlier voted for same person, this year vote share (in %) of A decreased by 2 2/9. If all the new voters voted for A, then the vote share of would have increased by 8 8/9. What is the number of voted casted to A present election?

In the previous election, 150000 voted for a constituency where only two candidates A and B contested. Due to awareness campaign, 20% more people voted this time. Assuming all people who voted earlier voted for same person, this year vote share (in %) of A decreased by 2 2/9. If all the new voters voted for A, then the vote share of would have increased by 8 8/9. What is the number of voted casted to A present election? Correct Answer 80000

Let the amount of votes casted to A in previous election be x

Amount of votes casted to B = 150000 – x

20% more people = 20/100 × 150000 = 30000 voters

Let y voters out the new voters vote for A

New voters who voted for B = 30000 – y

Change in vote share of A if all 30000 voted for A

(x + 30000) / (150000 + 30000) × 100 – x/150000 × 100 = 8 8/9 (80/9)

⇒ (x + 30000) /1800 – x/1500 = 80/9

⇒ {5 × (x + 30000) – 6 × x} /9000 = 80/9

⇒ (150000 – x) /9000 = 80/9

⇒ 150000 – x = 80000

⇒ x = 70000

Change in vote share originally

((x + y) /180000) × 100 – (x/150000) × 100 = -2 2/9 (-20/9)

⇒ x = 70000

⇒ (70000 + y) /1800 – 700/15 = -20/9

⇒ (70000 + y – 120 × 700) /1800 = -20/9

⇒ (y – 14000) /1800 = -20/9

⇒ y – 14000 = - 4000

⇒ y = 10000

∴ Total votes polled for A in this election = 70000 + 10000 = 80000

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