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)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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