2/5 of the voters promise to vote for A and the rest promised to vote for B. Of these, on the last day 15% of the voters went back of their promise to vote for A and 25% of voters went back of their promise for B. A lost by 200 votes. Then, the total number of voters is

The correct answer is (A) 10000.

• Mathematical Principle: Let the total number of voters be x. According to the problem, voters promised for A are (2/5)x and for B are (3/5)x. Deviations occur on the last day: 15% of A's supporters move to B, and 25% of B's supporters move to A.
• Step-by-Step Calculation: Final votes for A = (85% of 0.4x) + (25% of 0.6x) = 0.34x + 0.15x = 0.49x. Final votes for B = (75% of 0.6x) + (15% of 0.4x) = 0.45x + 0.06x = 0.51x. Given that A lost by 200 votes, the difference B - A = 200. Thus, 0.51x - 0.49x = 200, which simplifies to 0.02x = 200. Solving for x: x = 200 / 0.02 = 10000.
• Verification: If x = 10000, A starts with 4000 and B with 6000. After shifts, A receives 3400 (from original 4000) + 1500 (from B's switch) = 4900. B receives 4500 (from original 6000) + 600 (from A's switch) = 5100. The difference is 5100 - 4900 = 200, confirming A loses by 200 votes. Other options fail to satisfy this condition.