PrepRung
Sign inSign up free

CAT 2016 Slot 2 · Quant · Percentages · medium

In an election between two candidates, 20% of the registered voters did not vote, and 5% of the votes cast were declared invalid. The winner got 55%…

Single correct option

In an election between two candidates, 20% of the registered voters did not vote, and 5% of the votes cast were declared invalid. The winner got 55% of the valid votes and won by 1,520 votes. How many voters were registered?
  1. A. 18,000
  2. B. 19,000
  3. C. 20,000
  4. D. 25,000
Show answer and solution

Answer: (C) 20,000

Let N be the number of registered voters.
Votes cast = 0.8N. Valid votes = 0.95 × 0.8N = 0.76N.

The winner has 55% and the loser 45% of the valid votes, so the margin is 10% of the valid votes = 0.076N.

0.076N = 1520, so N = 20,000.

Tip: in a two-way contest, margin = (2 × winner's share − 100)% of the valid votes.
Report a mistake

Original question written in the CAT 2016 Slot 2 pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake