There are two candidates P and Q in an election. During the campaign, 40% of the voters promised to vote for P, and rest for Q. However, on the day of election 15% of the voters went back on their promise to vote for P and instead voted for Q. 25% of the voters went back on their promise to vote for Q and instead voted for P. Suppose, P lost by 2 votes, then what was the total number of voters?
Options:
(A) 100
(B) 110
(C) 90
(D) 95
Official Answer Key:
A
Step-by-Step Solution & Explanation
Let total voters = T. Initial P-promisers = 0.40T, of which 15% defect to Q, so P retains 0.85×0.40T = 0.34T. Initial Q-promisers = 0.60T, of which 25% defect to P, so P gains 0.25×0.60T = 0.15T, while Q retains 0.75×0.60T = 0.45T. Final P votes = 0.34T + 0.15T = 0.49T. Final Q votes = 0.45T + 0.15T(from P defectors to Q, 0.15×0.40T=0.06T) = 0.45T + 0.06T = 0.51T. P lost by 2 votes: 0.51T − 0.49T = 0.02T = 2 ⇒ T = 100, matching option (A).
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