Solutions
Given:
Winning candidate received 52% of the valid votes.
The winning candidate won by a margin of 360 votes.
10% of the votes were declared invalid.
Formula:
Let the total number of votes polled be denoted as "T".
Let the percentage of valid votes be denoted as "p" (which is 100% - 10% = 90%)
Let the number of valid votes be denoted as "V" (which is 90% of T).
Let the number of votes received by the winning candidate be denoted as "W" (which is 52% of V).
Let the number of votes received by the losing candidate be denoted as "L" (which is 48% of V).
Since the winning candidate won by a margin of 360 votes, we have:
W - L = 360
Solution:
Since the winning candidate received 52% of the valid votes, we have:
W = 52% of V
or
W = (52/100) × V
Similarly, the losing candidate received 48% of the valid votes, we have:
L = 48% of V
or
L = (48/100) × V
Substituting the values of W and L in the equation W - L = 360, we get:
(52/100) × V - (48/100) × V = 360
Simplifying the above equation, we get:
(4/100) × V = 360
or
V = (360 × 100)/4
or
V = 9000
Therefore, the total number of votes polled is:
T = V / 0.9 (since valid votes are 90% of total votes)
or
T = 9000 / 0.9
or
T = 10000
Hence, the total number of votes polled is 10000.