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In an election contested between two candidates, winner beat the loser by 5040 votes. If out of total votes cast, 16% were declared invalid and winner received 75% of the total valid votes, then find the number of invalid votes cast. Options 1920 1520 1740 1280

Question

In an election contested between two candidates, winner beat the loser by 5040 votes. If out of total votes cast, 16% were declared invalid and winner received 75% of the total valid votes, then find the number of invalid votes cast.

Options 1920

1520

1740

1280

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Solution

Vamos resolver o problema passo a passo.

  1. Vamos definir algumas variáveis:

    • T T = Total de votos
    • I I = Votos inválidos
    • V V = Votos válidos
    • W W = Votos recebidos pelo vencedor
    • L L = Votos recebidos pelo perdedor

  2. Sabemos que 16% dos votos foram declarados inválidos: I=0,16T I = 0,16T

  3. Portanto, os votos válidos são: V=T−I=T−0,16T=0,84T V = T - I = T - 0,16T = 0,84T

  4. O vencedor recebeu 75% dos votos válidos: W=0,75V=0,75×0,84T=0,63T W = 0,75V = 0,75 \times 0,84T = 0,63T

  5. O perdedor recebeu os votos válidos restantes: L=V−W=0,84T−0,63T=0,21T L = V - W = 0,84T - 0,63T = 0,21T

  6. A diferença de votos entre o vencedor e o perdedor é 5040: W−L=5040 W - L = 5040 Substituindo os valores de W W e L L : 0,63T−0,21T=5040 0,63T - 0,21T = 5040 0,42T=5040 0,42T = 5040 T=50400,42=12000 T = \frac{5040}{0,42} = 12000

  7. Agora, calculamos os votos inválidos: I=0,16T=0,16×12000=1920 I = 0,16T = 0,16 \times 12000 = 1920

Portanto, o número de votos inválidos é 1920.

Resposta: 1920

This problem has been solved

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