A, B and C are three parties which contests in local election (people vote for one of the three parties alone). A and B forms an alliance thinking that they will get 50% more votes than C due to which 20% of voters from party A vote for party C and 15000 votes from party B vote for party C. Now C gets 56 2/3% of the total vote casted whereas only 16 2/3% of the voters only voted for party B? What is the initial amount of vote bank that party A had before alliance? Correct Answer 50000 Let the amount of original vote bank for party A, B and C be a, b and c respectively. Due to alliance 20% of voters from A votes to party C and 15000 from party B to party C So, Remaining vote for A = 80% of a = 0.8a Remaining vote for B = b – 15000 Vote for C = c + 0.2a + 15000 % of vote of party C = ((c + 0.2a + 15000) / (a + b + c)) × 100 ⇒ (170/3) = ((c + 0.2a + 15000) / (a + b + c)) × 100 ⇒ 17/3 = ((c + 0.2a + 15000) / (a + b + c)) × 10 ⇒ 17a + 17b + 17c = 30c + 6a + 450000 ⇒ 11a + 17b = 13c + 450000 ---- 1 % vote by party B = ((b – 15000) / (a + b + c)) × 100 ⇒ 16 2/3 = ((b – 15000) / (a + b + c)) × 100 ⇒ 50/3 = ((b – 15000) / (a + b + c)) × 100 ⇒ a + b + c = 6b – 90000 ⇒ a + c = 5b – 90000 ---- 2 Given that (a + c) = 50% more than B a + b = 1.5c ⇒ a = 1.5c – b Substituting in equation 1 and 2, 16.5c – 11b + 17b = 13c + 450000 ⇒ 3.5c + 6b = 450000 ---- 3 ⇒ 1.5c – b + c = 5b – 90000 ⇒ 6b – 2.5c = 90000 ---- 4 Subtracting the equations 6c = 360000 ⇒ c = 60000 Substituting in equation 3 210000 + 6b = 450000 ⇒ b = 40000 ∴ a = 1.5c – b = 50000