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Question

In an election, $$10\%$$ of the people in the voter's list did not participate $$60$$ votes were declared invalid. There are only two candidates $$A$$ and $$B$$, $$A$$ defeated $$B$$ by $$308$$ votes It has found that $$47\%$$ of the people listed in the voter's list voted for $$A$$. Find the total number of votes polled.


A
6200
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B
5580
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C
6000
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D
7200
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Solution

The correct option is A $$5580$$
Let the number of votes $$A$$ gets $$=x$$
Then, by the given condition, 
the number of votes  $$B$$ gets $$=x-308$$.

$$60$$ votes were invalid.
$$\therefore $$ The total number of votes polled $$=x+x-308+60=2x-248$$........(i)

$$10\%$$ of the listed population refrained from voting.
$$\therefore $$ $$(100-10)\%=90\%$$ of the listed population took part in the election.

So, the total number of the listed population $$=$$ $$(2x-248)\times \dfrac { 100 }{ 90 } =\dfrac { 20x-2480 }{ 9 }. $$

$$47\%$$ of this  population voted for $$A$$.

$$\therefore $$ $$A$$ got $$\dfrac { 20x-2480 }{ 9 } \times \dfrac { 47 }{ 100 } =x$$

$$\Rightarrow 47(20x-2480)=900x$$
$$\Rightarrow 40x=116560$$
$$\Rightarrow x=2914$$

So, the total number of votes polled $$=2x-248$$  .....(from i)
$$=$$ $$2\times  2914-248=5580$$
Ans- Option B.

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