Question

In an election, candidate A got 75% of the total valid votes. If 15% of the total votes were declared invalid and the total numbers of votes is 560000, find the number of valid votes polled in favour of the candidate.
A) 357000
B) 365796
C) 375000
D) 500000

Answer 1

Hint: Form the mathematical equation according to the given language in question.
 A percentage is a number or ratio that represents a fraction of 100. It is denoted by the symbol “%”.
While solving ‘x% of y’, keep in mind that:
% means = divide by hundreds
of means = multiplication ‘$ \times $’.
To find the numbers of votes of a candidate it is necessary to find the numbers of valid votes.

Complete step by step solution:
Step 1
Given information:
Total numbers of votes = 560000
Percentage of invalid votes = 15%
And, candidate A got = 75 % of valid votes.

Step 2: Finding the numbers of invalid votes.
We know,
% (percentage) of declared invalid votes = 15% of total votes
Numbers of declared invalid votes: = 15% of total votes
$ \Rightarrow {\text{ = }}\dfrac{{15}}{{100}} \times 560000$
\[
   \Rightarrow {\text{ = }}\dfrac{{15}}{{1{{00}}}} \times 5600{{00}} \\
   \Rightarrow {\text{ }} = 84000{\text{ }} \\
 \]

Step 3: To find the numbers of valid votes
Hence, total numbers of valid votes = total numbers of votes – numbers of declared invalid votes
                                                                = 560000 – 84000
                                                                = 476000

Step 4: To find numbers of votes of candidate A
We know,
Candidate A got % (percentage) of votes = 75% of valid votes
Numbers of votes, candidate A got = 75% of valid votes
\[
   \Rightarrow {\text{ = }}\dfrac{{75}}{{100}} \times 476000 \\
   \Rightarrow {\text{ = }}\dfrac{{75}}{{1{{00}}}} \times 4760{{00}} \\
   \Rightarrow {\text{ }} = 357000 \\
 \]

Therefore, Candidate A got a total of 357000 valid votes. Thus, the correct option is (A).

Additional information: Increased or more than x% indicates the addition of x% of y to y; reduced or less than x% indicates the subtraction of x% of y from y.

Note:
To convert from Percentage to fraction or decimal, it is divided by 100.
For example: convert 50% to decimal.
Solution $50\% = \dfrac{{50}}{{100}}$
                         = 0.5
Convert 50% to fraction
Solution $50\% = \dfrac{{5{0}}}{{10{0}}}$
                           $ = \dfrac{1}{2}$.
To convert decimal or fraction to percentage, it is multiplied by 100.
For example: convert 0.35 into percentage.
Solution $0.35{\text{ into percentage}} = 0.35 \times 100$
                                                        = 35%
Convert $\dfrac{2}{5}$into percentage.