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      Question

      Average runs scored by 11 players in a match were 35.

      Average runs scored by players except Virat and Rohit, was 26. Runs scored by Virat were 53 more than that by Rohit. If Virat scored all the runs by hitting fours (4 runs) and sixes (6 runs) , then find the number of sixes hit by Virat. (Note: Virat played 20 balls only and he either hits six or four on each ball) 
      A 11 Correct Answer Incorrect Answer
      B 13 Correct Answer Incorrect Answer
      C 7 Correct Answer Incorrect Answer
      D 8 Correct Answer Incorrect Answer
      E 9 Correct Answer Incorrect Answer

      Solution

      Runs scored by all the 11 players = 35 X 11 = 385
      Runs scored by all the players except Rohit and Virat = 26 X 9 = 234
      Sum of Runs scored by Rohit and Virat = 385 - 234 = 151
      Let the runs scored by Rohit be 'y'.
      So, runs scored by Virat = y + 53
      Now, y + y + 53 = 151
      Or, 2y = 98
      Or, 'y' = 49
      So, runs scored by Virat = 49 + 53 = 102
      Let the number of sixes hit by Virat be 'a'.
      So, 6a + 4 X (20 - a) = 102
      Or, 6a + 80 - 4a = 102
      Or, 2a = 102 - 80 = 22
      Or, 'a' = 11
      Therefore, number of sixes hit by Virat = 11

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