Question

A, B, and C contest an election from a particular constituency. A and B together got 50% more votes than C. The vote share of A and C together is 30 percentage points more than the vote share of B. Who won the election?

Answer 1

Answer:

c won

Explanation:

Let a,b,c be the  vote  share  of  A, B, C  respectively

a + b  =  1.5 c

a + c   =  b + 30

a + b + c   = 100,    2b + 30 =  100,

b  =  35

a  =   25,  c =  40,  So, C  won  the  election.

Answer 2

Answer:

The winner of the election is found to be the candidate B.

Explanation:

We are given that the total votes obtained by A and B are 50% more than that obtained by C, representing this mathematically, we get:

$A+B=C+\frac{50}{100}C$

$A+B=C+0.5C$

$A+B=1.5C$                       ...(i)

Similarly, the total votes obtained by A and C are 30% more than that obtained by B, representing this mathematically, we get:

$A+C=B+0.3B$

$A+C=1.3B$                       ...(ii)

by (i) and (ii), equating the values of A, we get:

$1.5C-B=1.3B-C$

$1.5C+C=1.3B+B$

$2.5C=2.3B$

$C=0.92B$                             ...(iii)

Substituting C in (i), we get:

$A+B=1.5(0.92B)$

$A=1.38B-B$

$A=0.38B$                             ...(iv)  

We can clearly see from (iii) and (iv), that both A and C have obtained less votes than the candidate B. Thus, B is the winner of the election.

#SPJ3