The average of a batsman who played a certain number of innings is 48 before playing his last match. In the last match he played, he scored 103 before getting out. If the average of his score after this innings becomes a prime number less than 60, what is the sum of all the possible number of matches played by the batsman?

16

Let batsmen played 'x' matches and avg is 48..so total runs =48x Next match score = 103 So total of (48x+103) runs in (x+1) match So new average = (48x+103) / (x+1)........... 1 And this value is a prime number less than 60..so only possible values r 53 and 59 as average won't be less than48. So equating 1 with 53... x =10 Equating 1 with 59....x= 4 Sum of possible matches so = x+1= 11+5=16

(48(x-1) + 103)/x = 53 or 59 gives x = 11 & 5 => sum = 16