In an election between two candidates, the winner has a margin of 10% of the votes polled. If 1500 people change their mind and vote for the loser, the loser would have won by a margin of 10% of the votes polled. Find the total number of votes polled in the election?  Choose the correct choice from the following choices
A) 30,000  B) 15,450  C) 45,000  D) 60,000  E) 15,000

Rationale: "total # of votes cast = 100 x , out of these , let the # of votes won by the winner = w , and for the loser ( l ) = 100 x - w . given that w - ( 100 x - w ) = 10 % of total votes cast = 10 x thus , 2 w - 100 x = 10 x → → w = 55 x and l = 100 x - 55 x = 45 x . according to the new condition , if the loser had won 45 x + 1500 votes , then , ( 45 x + 1500 ) - ( 55 x - 1500 ) = 10 % of total votes cast = 10 x thus , 3000 = 20 x and 100 x = 15000 answer : e"
Answer: E