Question

in an election contest between  A and B ,A obtained votes equal to the twice the number of persons on the electoral roll who did not cast their votes, and this later number was equal to twice his majority over B. if there were 18000 persons on the electoral roll, how many voted for B?

Answer 1

Sol: Let the number of people who did'nt voted be x.
Now the number of people who voted = 18000-x
Number of votes given to A = 2 × x = 2x   .......As  per the queston
Number of votes given to B = Total no. of voters - Total number of votes given to A.
i.e.  No. of votes given to B = [18000-x]-2x
Now As given in the que., x is equal to the twice of majority got by A.
Majority got by A = Total no. votes given to A - Total votes given to B.
i.e.                                 2x-[18000-x-2x]
So,
x = 2{2x-[18000-x-2x]}
x = 2{2x - 18000 + 3x}
x = 2{5x - 18000}
x = 10x - 36000
9x = 36000
x = 4000
So, No. of votes given to B = 18000-x-2x = 18000-4000-2×4000 = 18000-12000 = 6000 votes.

Answer 2

Let the number of those who did not vote = x

Those who voted = (18000 - x)

A obtained = 2x

B obtained the number who voted less the number A got

= (18000 - x) - 2x = 18000 - 3x

Majority over B = A votes -  B votes

                         = 2x - (18000 - 3x)

                         = 5x - 18000

"this later number was equal to the twice his majority over B"

From this statement;

x = 2(5x - 18000)

x - 10x = -36000

9x = 36000

x = 4000

B got (8000 - 3x) votes = 18000 - 3(4000)

                                     = 6000 votes

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