Question

# In an election contested between A and B, A obtained was equal to 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?

Solution

## Let the number of votes for A be x and the number of votes for B be y. ⇒ The number of persons who did not vote = (18000 � x � y) Given A obtained votes equal to twice the number of persons on the electoral roll x = 2(18000 � x � y) x = 36000 � 2x � 2y ⇒ 3x + 2y = 36000 → (1) It is also given that A got votes twice his majority over B. ⇒ (18000 � x � y) = (2) (x � y) ⇒ (18000 � x � y) = 2x � 2y ⇒ 2x � 2y + x + y = 18000 ⇒ 3x � y = 18000 → (2) Subtract (2) from (1), we get 3x + 2y = 36000 3x � y = 18000 ______________ 3y = 18000 ∴ y = 6000 Put y = 6000 in 3x � y = 18000 3x = 18000 + 6000 = 24000 ∴ x = 8000 ∴Hence number of votes for B = 6000  Mathematics

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