Question

In an election, a candidate secured \[58\% \] of votes polled and won the election by \[18,336\] votes. Find the total number of votes pulled and votes secured by each candidate.
A. \[1,14,560;66,728;48,112\]
B. \[1,14,800;66,168;48,232\]
C. \[1,14,200;66,668;48,032\]
D. \[1,14,600;66,468;48,132\]

Answer 1

Hint:We solve this question by assuming total number of votes as a variable and then using the concept of percentage we calculate number of votes by the candidates, form a relation subtracting number of votes by second candidate from number of votes by the first candidate and equate it to the number of votes first candidate won by.
* Percentage of any number can be solved by the formula \[x\% \] of \[m = \dfrac{x}{{100}} \times m\]

Complete step-by-step answer:
Let us assume total number of votes as \[x\]
We know the first candidate scored \[58\% \] of the total votes.
Then we can calculate the number of votes secured by the first candidate as \[58\% \] of \[x\].
\[58\% \] of \[x = \dfrac{{58}}{{100}} \times x = \dfrac{{58x}}{{100}}\]
Similarly, We know the first candidate scored \[58\% \] of the total votes.
Therefore, Percentage of votes scored by the second candidate is \[100\% - 58\% = 42\% \]
Then we can calculate the number of votes secured by the second candidate as \[42\% \] of \[x\].
\[42\% \] of \[x = \dfrac{{42}}{{100}} \times x = \dfrac{{42x}}{{100}}\]
Using the information given in the question, the first candidate won the election by \[18,336\] votes
Therefore, we can say that the first candidate had \[18,336\] more votes than the second candidate.
Number of votes of first candidate – number of votes of second candidate\[ = 18,336\]
 \[\dfrac{{58x}}{{100}} - \dfrac{{42x}}{{100}} = 18336\]
Taking LCM on LHS of the equation
\[
  \dfrac{{58x - 42x}}{{100}} = 18336 \\
  \dfrac{{16x}}{{100}} = 18336 \\
 \]
Shift the denominator from LHS to the numerator of RHS by cross multiplication.
\[
  16x = 18336 \times 100 \\
  16x = 1833600 \\
 \]
Dividing both sides of the equation by \[16\]
\[
  \dfrac{{16x}}{{16}} = \dfrac{{1836600}}{{16}} \\
  x = 1,14,600 \\
 \]
Therefore, total number of votes in the election are \[1,14,600\]
Now we can calculate \[58\% \] of total votes i.e. \[1,14,600\]
\[\dfrac{{58}}{{100}} \times x = \dfrac{{58}}{{100}} \times 1,14,600\]
Cancel out the terms from denominator and numerator
\[\dfrac{{58 \times 114600}}{{100}} = 58 \times 1146 = 66468\]
Therefore number of votes secured by first candidate are \[66,468\]
Similarly, we can calculate \[42\% \] of total votes i.e. \[1,14,600\]
\[\dfrac{{42}}{{100}} \times x = \dfrac{{42}}{{100}} \times 1,14,600\]
Cancel out the terms from denominator and numerator
\[\dfrac{{42 \times 114600}}{{100}} = 42 \times 1146 = 48132\]
Therefore number of votes secured by second candidate are \[48,132\]
Thus, option D is correct.

Note:Students are likely to make mistakes while calculating the percentage part where they don’t cancel out the numerator and denominator by \[100\] first which makes the calculation part difficult.
Also, we can check the answer of percentage by comparing it to the total number of votes as the percentage of any number will always be less than that number.