percentage

Question

In an election between two candidates 10% of the votes polled were invalid. If the winning candidate got 52% of the total valid votes and wins by a majority of 160 votes, then how many valid votes other candidate got?

(a) 1800  (b) 1600

(c) 1920  (d) 2220

Answer 1

Consider $100x$ votes polled in total.

Then $90x$ were valid & $10x$ were invalid.

Then winner got $\left ( \frac{52}{100} \times 90x \right )$ votes & loser got $\left ( \frac{48}{100} \times 90x \right )$ votes.

It is given that the diffrence of votes b/w winner & loser is $160$,

that is $\left ( \frac{52}{100} \times 90x \right ) - \left ( \frac{48}{100} \times 90x \right ) = 160$

On simplifying this we get

$\left ( \frac{48}{100} \times 90x \right ) = 1920$.

Hence loser got $1920$ votes.

Comments

4% is 160, so 48% = 160*12 = 1920