Answer

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**Hint:**Find total valid votes first and then check the % of both candidates and subtract 65% from 100% for Mahtre’s vote %.

To find the percentage the formula is:

$\dfrac{\text{given amount}}{\text{total amount}}\times 100$

And to find amount from a given percentage the formula is:

$\dfrac{\text{amount}\,\text{in}\,\text{percentage}(a{\scriptstyle{}^{0}/{}_{0}})\times \text{total}\,\text{amount}\,\text{of}\,\text{that}\,\text{percentage}}{100}$

**Complete step by step solution:**Given that, the number of candidates is 2.

namely Bhiku and Mhatre.

Bhiku get 65% of the total valid votes

The total number of votes = 6000.

Total number of invalid votes = 25% of 6000

$=\dfrac{25}{1{0}{0}}\times 60{0}{0}=1500$

Therefore no. of invalid votes = 1500

Valid votes = 6000 − 1500 = 4500

Now, total valid votes = 4500.

Bhiku got 65% of valid votes

Therefore total number of votes or valid votes of Bhiku =

65% of 4500

$\begin{align}

& \Rightarrow \dfrac{65}{1{0}{0}}\times 45{0}{0} \\

& \Rightarrow 2,925\ \text{votes} \\

\end{align}$

And percentage (%) of valid votes of Mhatre = 35%

Therefore votes of Mhatre = 35 of 4500

\[\begin{align}

& =\dfrac{35}{1{0}{0}}\times 45{0}{0} \\

& =1575\ \text{votes} \\

\end{align}\]

= 1575 votes

Hence, the valid number of votes of Mhatre = 35% and in count it is 1575 votes.

**Note:**In this type of question, only simple logic is required is subtraction and finding the percentage of appropriate amount. One variation of this question is instead of voters they’ll give the percentage population and we need to tell the count. So, there can be many variations of questions. We just need to stick to our concept.

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