In an election only two candidates contested 30% of the voters did not vote and 130 votes were declared invalid the winner got 300 votes more than his opponent thus he secured 45% votes of the total on voter list . Approximate % votes of the defeated candidate out of the votes casted is
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Answers
Answer:
Defeated candidate got %age votes = 27.35 %
Step-by-step explanation:
Voters who did not cast votes = 30%
Voters who cast their votes = 70 %
Let the number of votes of defeated candidate = x
Then the number of the votes of the winner = x + 300
Then x + 300 = 45 % ............... (i)
Numbers of votes that were declared invalid = 130
Then according to the given condition
x + (x +300) + 130 = 70 %
x + 45 % + 130 = 70 %
x + 130 = 70 % - 45 %
x + 130 = 35 % ..................... (ii)
(i) - (ii) ⇒ (Subtracting ii from i implies that)
170 = 10 %
10 % = 170
1 % = 17
multiplying both side by 45 , we get
45 % = 765 , putting this in (i), we get
x + 300 = 765
x = 765 - 300
x = 465
Defeated candidate got votes = 465 ( ∵ 17 votes correspond to 1 %)
Dividing 465 by 17 , we get
Defeated candidate got %age votes = 27.35 %
Answer:The percentage of the defeated is 13.8 %
Step-by-step explanation: Let be the registered voters be X
Voters cast = 70 x÷ 100
Valid voters =70 x÷ 100 - 130
Winner votes = 45 x ÷ 100
So, the loser vote = valid vote - winner votes
70 x÷ 100 - 130 - 45 x ÷ 100
= 25 x ÷100 - 130
To find out the total number of votes
45 x ÷ 100 (25 x÷ 100 - 130) = 300
45 x÷ 100 -25 x ÷100 = 300 -130
20 x ÷ 100 =170
x = 170 ×100 ÷20
x= 850
So, the total number of votes are 850
Registered votes = 70 x ÷ 100
= 70× 850 ÷ 100
= 595
Votes of defeated candidate = 25 x ÷ 100 - 130
= 25 × 850 ÷ 100 -130
=212.5 - 130
= 82.5
The percentage of the defeated candidates = 82.5 ÷ 595 × 100
= 13.8 %