A batsman has a certain average in 59 innings that he has played till the last one. If his average increased by 2 runs after scoring 181 in the last innings, what is his average after these 60 innings?
Question
A batsman has a certain average in 59 innings that he has played till the last one. If his average increased by 2 runs after scoring 181 in the last innings, what is his average after these 60 innings?
Solution
Step 1: Let's denote the initial average (before the last innings) as 'x'. This means the total runs scored in 59 innings is 59x.
Step 2: After scoring 181 in the last innings, the total runs become 59x + 181.
Step 3: The new average after 60 innings is x + 2.
Step 4: The average is calculated by dividing the total runs by the number of innings. So, we can set up the equation: (59x + 181) / 60 = x + 2.
Step 5: Solve this equation for 'x'.
First, multiply both sides by 60 to get rid of the denominator on the left side: 59x + 181 = 60x + 120.
Step 6: Rearrange the equation to isolate 'x': 60x - 59x = 181 - 120.
Step 7: Simplify the equation to find 'x': x = 61.
So, the initial average before the last innings was 61 runs.
Step 8: To find the new average after 60 innings, add 2 to the initial average: 61 + 2 = 63.
Therefore, the batsman's average after these 60 innings is 63 runs.
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