Problem: in an election contested by two parties , party d secured 12 % of the total votes more than party r . if party r got 132000 votes , by how many votes did it lose the election ?
Rationale: explanatory answer let the percentage of the total votes secured by party d be x % then the percentage of total votes secured by party r = ( x - 12 ) % as there are only two parties contesting in the election , the sum total of the votes secured by the two parties should total up to 100 % i . e . , x + x - 12 = 100 2 x - 12 = 100 or 2 x = 112 or x = 56 % . if party d got 56 % of the votes , then party got ( 56 - 12 ) = 44 % of the total votes . 44 % of the total votes = 132,000 i . e . , 44 / 100 * t = 132,000 = > t = 132000 * 100 / 44 = 300,000 votes . the margin by which party r lost the election = 12 % of the total votes = 12 % of 300,000 = 36,000 . the correct choice is ( d )
annotated_formula: multiply(divide(132000, divide(subtract(const_100, 12), const_2)), 12)