Three candidates X, Y and Z participated in an election. X got 30% more votes than Y, whereas Z got 25% more votes than Y. X also overtook Z by 5000 votes. If 71% of the voters voted and no invalid votes were cast, then what was the total number of voters in the voting list?

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Accepted Answer

Let the number of votes received by Y be y.

Then votes received by X = y + 30% of y = y + 0.3y = 1.3y
Votes received by Z = y + 25% of y = y + 0.25y = 1.25y

Given, X overtook Z by 5000 votes:
1.3y - 1.25y = 5000
0.05y = 5000
=> y = 5000 / 0.05 = 100000

Total votes polled = X + Y + Z = 1.3y + y + 1.25y = (1.3 + 1 + 1.25)y = 3.55y
= 3.55 * 100000 = 355000

Given 71% of voters voted, so total number of voters = Total votes polled / 0.71
= 355000 / 0.71 ≈ 500000

Therefore, the total number of voters in the voting list is 5,00,000.

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