A batsman played 11 innings and has a certain average.This average increases by 2 runs when his 3 innings of 32 runs, 33 runs and 34 runs are replaced by 3 other innings.Find the average of these 3 new innings.40 runs35(3/8) runs42(3/8) runs40(1/3) runs
Question
A batsman played 11 innings and has a certain average.This average increases by 2 runs when his 3 innings of 32 runs, 33 runs and 34 runs are replaced by 3 other innings.Find the average of these 3 new innings.40 runs35(3/8) runs42(3/8) runs40(1/3) runs
Solution
Let's solve this step by step:
Step 1: Let's assume the total runs scored in the 11 innings is 'x' and the average is 'y'. So, x/11 = y.
Step 2: When the 3 innings of 32, 33 and 34 runs are replaced by 3 other innings, the total runs become 'x - 32 - 33 - 34 + 3p' (where 'p' is the average of the 3 new innings).
Step 3: The new average becomes 'y + 2'. So, (x - 32 - 33 - 34 + 3p)/11 = y + 2.
Step 4: Substituting the value of 'y' from step 1, we get (x - 99 + 3p)/11 = x/11 + 2.
Step 5: Simplifying the above equation, we get 3p = 99 + 22.
Step 6: So, p = (99 + 22)/3 = 121/3 = 40(1/3) runs.
So, the average of the 3 new innings is 40(1/3) runs.
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