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Three parties A, B and C contest the election. From the previous election, 4000 voters who voted for party C voted for B and 2000 from party C voted for party A. 2000 voters from party B voted for C and 1000 voters did not vote at all. In previous election C won the election defeating B by 5000 votes and defeated A by 15000 votes. The percentage amounts of vote poled to party A in the present election is 300/11. What is the vote obtained by party A in the present election?

Three parties A, B and C contest the election. From the previous election, 4000 voters who voted for party C voted for B and 2000 from party C voted for party A. 2000 voters from party B voted for C and 1000 voters did not vote at all. In previous election C won the election defeating B by 5000 votes and defeated A by 15000 votes. The percentage amounts of vote poled to party A in the present election is 300/11. What is the vote obtained by party A in the present election? Correct Answer 27000

Let the total number of votes polled to party A, B and C in the previous election be a, b and b + 5000 respectively.

New votes polled to A = a + 2000

New votes polled to B = b + 4000 – 2000 – 1000

⇒ b + 1000

New votes polled to C = b + 5000 – 4000 – 6000 + 2000

⇒ b + 1000

% vote by A = ((a + 2000)/(a + 2000 + b + 1000 + b + 1000)) × 100

⇒ 300/11 = ((a + 2000)/(a + 2b + 4000)) × 100

⇒ 3/11 = (a + 2000)/(a + 2b + 5000)

⇒ 3a + 6b + 12000 = 11a + 22000

⇒ 6b – 8a = 10000      ---- 1

Vote difference between A and C = b + 5000 – a = 15000

⇒ b – a = 10000     ---- 2

Solving, Equation 1 – 6 × Equation 2,

-2a = -50000

⇒ a = 25000

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