  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  B
5580  C
6000  D
7200  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.Maths

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