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In an athletics meet, 8 runners—Arun, Barun, Chandan, Dharam, Ezhil, Farhan, Govind, and Harman— participated in three races: 100 m, 200 m, and 400 m. No runner finished in the same position in any of the races. In each of the three races, all runners finished in distinct positions from 1 to 8. Position 1 is given to the runner who completed the race 1st, Position 2 is given to the runner who completed the race 2nd and so on. The following information is known about these races:(i) In 100 m race, Chandan finished 3rd, and in 400 m race, he finished 2nd. In 100 m and 200 m races, Barun finished 1st and 2nd, respectively.(ii) In 400 m race, Arun did not finish 4th, but Govind finished 7th in 200 m race. In 400 m race, Harman did not finish 4th, and Farhan did not finish 8th.(iii) For Arun, the number of people who finished ahead of him in 100 m race is the same as the number of people who finished behind him in 200 m race.(iv) In every race, Dharam, Ezhil, and Farhan finished in consecutive positions, with Dharam finishing first among them and Farhan finishing last.(v) Across the three races, the sum of Dharam’s positions is the same as the sum of Govind’s positions.(vi) Harman had his best finish in 400 m

Question

In an athletics meet, 8 runners—Arun, Barun, Chandan, Dharam, Ezhil, Farhan, Govind, and Harman— participated in three races: 100 m, 200 m, and 400 m. No runner finished in the same position in any of the races. In each of the three races, all runners finished in distinct positions from 1 to 8. Position 1 is given to the runner who completed the race 1st, Position 2 is given to the runner who completed the race 2nd and so on. The following information is known about these races:(i) In 100 m race, Chandan finished 3rd, and in 400 m race, he finished 2nd. In 100 m and 200 m races, Barun finished 1st and 2nd, respectively.(ii) In 400 m race, Arun did not finish 4th, but Govind finished 7th in 200 m race. In 400 m race, Harman did not finish 4th, and Farhan did not finish 8th.(iii) For Arun, the number of people who finished ahead of him in 100 m race is the same as the number of people who finished behind him in 200 m race.(iv) In every race, Dharam, Ezhil, and Farhan finished in consecutive positions, with Dharam finishing first among them and Farhan finishing last.(v) Across the three races, the sum of Dharam’s positions is the same as the sum of Govind’s positions.(vi) Harman had his best finish in 400 m

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Solution

Para resolver este problema, sigamos los pasos uno por uno:

  1. Información dada:

    • Chandan terminó 3º en la carrera de 100 m y 2º en la carrera de 400 m.
    • Barun terminó 1º en la carrera de 100 m y 2º en la carrera de 200 m.
    • Arun no terminó 4º en la carrera de 400 m.
    • Govind terminó 7º en la carrera de 200 m.
    • Harman no terminó 4º en la carrera de 400 m.
    • Farhan no terminó 8º en la carrera de 400 m.
    • Para Arun, el número de personas que terminaron antes que él en la carrera de 100 m es el mismo que el número de personas que terminaron después de él en la carrera de 200 m.
    • Dharam, Ezhil y Farhan terminaron en posiciones consecutivas en cada carrera, con Dharam terminando primero entre ellos y Farhan terminando último.
    • La suma de las posiciones de Dharam en las tres carreras es igual a la suma de las posiciones de Govind.
    • Harman tuvo su mejor posición en la carrera de 400 m.
  2. Carrera de 100 m:

    • Barun: 1º
    • Chandan: 3º
  3. Carrera de 200 m:

    • Barun: 2º
    • Govind: 7º
  4. Carrera de 400 m:

    • Chandan: 2º
  5. Posiciones de Arun:

    • Si el número de personas que terminaron antes que Arun en la carrera de 100 m es igual al número de personas que terminaron después de él en la carrera de 200 m, entonces Arun debe haber terminado en la misma posición en ambas carreras. Llamemos a esta posición X.
    • Posibles valores de X: 1, 2, 3, 4, 5, 6, 7, 8.
    • Pero Barun ya es 1º en 100 m y 2º en 200 m, y Chandan es 3º en 100 m, así que Arun no puede ser 1º, 2º o 3º en 100 m.
    • Arun no puede ser 4º en 400 m, así que Arun no puede ser 4º en 100 m.
    • Entonces, Arun puede ser 5º, 6º

This problem has been solved

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