Question

There was direct contest between two students for the post of president of Student Council of a school. If the winner got 55% vote and won by 70 votes then (i) how many valid votes were cast and (ii) how much vote the runner received?​

Answer 1

We have:-

• A contest between two students.
• The winner got 55% vote & won by 70 votes.

To FinD:-

• How many valid votes were cast and
• How much vote the runner received?

Solution:-

Let the total no. of valid votes be x.

According to the question candidate who got 55% vote, won the contest by 70 votes. And, the % of loosers was 100% - 55% = 45%

That means,

• Votes recieved by the winner - Votes recieved by the loser = 70 votes.

Then,

⇒ 55% of x - 45% of x = 70

⇒ 55/100 × x - 45/100 × x = 70

⇒ x( 55/100 - 45/100) = 70

⇒ x × 10/100 = 70

⇒ x / 10 = 70

⇒ x = 700

Now the winner got 55% of the votes i.e.

⇒ 55/100 × 700

⇒ 55 × 7

⇒ 385

Hence:-

• The total number of valid votes is 700
• And the total no. of votes received by the winner is 385.

Answer 2

Hlw !

Question :-

There was direct contest between two students for the post of president of Student Council of a school. If the winner got 55% vote and won by 70 votes then

• how many valid votes were cast and
• how much vote the runner received?

Given :-

• % of votes given to the winner = 50%
• Winner won by = 70 votes

this means that :-

Votes given to the winner - votes given to the loser = 70

To find :-

• Total votes casted
• how much did winner got.

Solution:-

let us assume the no. of votes be X.

% of votes loser got = 100% - 55% = 45%

now,

$\implies{rm }$ 55% of X - 45% of X = 70

$⇒\frac{55}{100} \times x - \frac{45}{100} \times x = 70 \\ ⇒x( \frac{55}{100} - \frac{45}{100} ) = 70 \\⇒ x \times \frac{10}{100} = 70 \\⇒ x = 700$

⇒Hence, the total votes casted were 700.

⇒ To find Votes got by the winner:-

55/100×700 = 385.

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Hope it helps ⭐⭐⭐