Question:
$\frac{2}{5}$ of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back on their promise to vote for P and 25% of voters went back on their promise to vote for Q, and P lost by 2 votes. Then the total number of voters is:
$\frac{2}{5}$ of the voters promise to vote for P and the rest promised to vote for Q. Of these, on the last day 15% of the voters went back on their promise to vote for P and 25% of voters went back on their promise to vote for Q, and P lost by 2 votes. Then the total number of voters is:
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Track vote changes step-by-step: losses from one side are gains to the other in such switching problems.
Updated On: Aug 6, 2025
- 100
- 110
- 90
- 95
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The Correct Option is A
Solution and Explanation
Step 1: Let total voters = N.
Voters for P initially = $(2/5)N$, for Q = $(3/5)N$.
Step 2: Voter changes
P loses 15% of $(2/5)N$ → loss = $(0.15 \times 2N/5) = 0.06N$.
Q loses 25% of $(3/5)N$ → loss = $(0.25 \times 3N/5) = 0.15N$.
Step 3: New votes
P's final votes = $(2N/5) - 0.06N + 0.15N$ (gained from Q's switch).
Q's final votes = $(3N/5) - 0.15N + 0.06N$.
Step 4: Given P lost by 2 votes
So Q's votes - P's votes = 2.
$[(3N/5) - 0.15N + 0.06N] - [(2N/5) - 0.06N + 0.15N] = 2$.
Simplify: $(0.6N - 0.09N) - (0.4N + 0.09N) = 2$.
$0.51N - 0.49N = 2$ → $0.02N = 2$ → $N = 100$.
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