Q.5

There are two candidates P and Q in an election. During the campaign,
40% of the voters promised to vote for P, and the 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

Election word problems with vote switches test percentage calculations and algebra, common in GATE, CAT, and quantitative aptitude sections. Here, 40% promised P (rest Q), but 15% of P’s switched to Q, 25% of Q’s to P, and P lost by 2 votes.

The correct answer is (A) 100, yielding integer voters: P gets 49 votes, Q 51.

Step-by-Step Solution

Let total voters = $T$.

• P promised: $0.4T$

• Q promised: $0.6T$

P actual votes:

• Stays with P: $0.85\times 0.4T=0.34T$

• Switches from Q: $0.25\times 0.6T=0.15T$

• Total P: $0.34T+0.15T=0.49T$

Q actual votes:

• Stays with Q: $0.75\times 0.6T=0.45T$

• Switches from P: $0.15\times 0.4T=0.06T$

• Total Q: $0.45T+0.06T=0.51T$

Q – P = 2 → $0.51T-0.49T=0.02T=2$ → $T=2/0.02=100$.

For T=100: P promised=40 (stays 34, +15 from Q)=49; Q promised=60 (stays 45, +6 from P)=51. Diff=2.

Why Other Options Fail

Only T=100 gives integers and exact 2-vote loss:

• (A) 100: Works perfectly (49 vs 51).

• (B) 110: P promised=44, 15% switch=6.6 (non-integer voters).

• (C) 90: P promised=36, 15% switch=5.4 (non-integer).

• (D) 95: P promised=38, 15% switch=5.7 (non-integer).

Quick Verification Table

Ideal for bioinformatics data modeling too. Verify: $0.02T=2$, T=100.