Question : The average number of runs scored by a cricketer in his 99 innings is 99. How many runs will he have to score in his 100th inning so that his average of runs in 100 innings may be 100?
Option 1: 100
Option 2: 99
Option 3: 199
Option 4: 101
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Correct Answer: 199
Solution : Given: Average runs are 99, total innings is 99 and new average is 100. According to the question, Let $x$ be the score in the 100 th inning. The total runs scored in 99 innings = 99 × 99 Total runs scored in 100 innings = $(99 × 99) + x$ ---(i) The total runs should be 100 × 100 after 100 th innings so that the average will be 100. The total runs scored in 100 th innings = 100 × 100 = 10000 ---(ii) From equation (i) and equation (ii), we get $10000 = (99 × 99) + x$ $x = 10000 - 9801$ $\therefore x = 199$ Hence, the correct answer is 199.
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