After the elections, a firm conducted a survey. Exactly 3% of the male voters said they had voted for candidate A, while exactly 47% of the female voters said they had voted for candidate A. If in total, exactly 19% of the people said they had voted for the Candidate. What is the minimum number of people who were surveyed?
Explanation:
Let the number of men be m and women be w.
Number of women selecting candidate A = 47% of w = 0.47w Number of men selecting candidate A = 3% of m = 0.03m
⇒ 0.03m + 0.47w = 0.19(m + w) ⇒ 0.28w = 0.16m ⇒ w : m = 4 : 7
Hence, w = 4x, m = 7x where x is an integer.
Number of women selecting candidate A = 47% of 4x = 4x × 47/100 = 47x/25 Number of men selecting candidate A = 3% of 7x = 7x × 3/100 = 21x/100
Now, both 47x/25 and 21x/100 must be integers, hence least possible value of x = 100.
∴ Least Total population is 4x + 7x = 11x = 1100
Hence, 1100.
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