Question

In an election 5% of the votes cast are declared invalid. A candidate gets 60% of total votes and wins the election by 760 votes. Find the total number of votes cast.​

Answer 1

$\bf\huge\underline\red{Answer}$

The total number of votes cast are 3040 respectively.

Explanation :-

Given :

• Percentage of votes declared invalid - 5%
• Percentage of votes of winning candidate - 60%
• No. of votes the winning candidate won by - 760

To find :

The total number of votes cast.

Solution :

Percentage of votes valid => (100 - 5)% = 95%

Percentage of votes of the losing candidate => (95 - 60%) = 35%

Difference between the percentage of votes => (60 - 35)% = 25%

According to question,

$= > 25\% \: of \: x \: = 760$

$= > \dfrac{25}{100} \times x = 760$

$= > \dfrac{25x}{100} = 760$

$= > x = \dfrac{760 \times 100}{25}$

$= > x = 3040$

Hence, the total number of votes is 3040

Answer 2

» In an election 5% of the votes cast are declared invalid.

• Let total number of votes be M.

Valid votes = 5% ____ [ GIVEN ]

Means number of votes = 100

So ..

Valid votes = 100% - 5% = 95%

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» A candidate gets 60% of total votes.

We have valid votes = 95% and a candidate gets 60% means we have to find how many votes he/she loose.

Loose votes = 95% - 60% = 35%

The difference of votes is 25%

( Means..

Difference = Valid votes - Loose votes

=> 95% - 35% = 25% )

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» He/she wins the election be 760 votes.

A.T.Q.

→ 25% of votes = 760

And we let the number of votes = M

→ 25% of M = 760

→ $\dfrac{25}{100}$ × M = 760

→ $\dfrac{M}{4}$ = 760

→ M = 760 × 4

→ M = 3040

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Total number of votes cast = 3040

___________ [ ANSWER ]

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