Question
The average of 40 numbers is 52. The average of the
first 25 numbers is 48 and the average of the last 25 numbers is 56. Find the average of the 10 numbers that are counted in both groups (i.e., the overlapping 10 numbers).Solution
Total sum of 40 numbers = 40 × 52 = 2080 Sum of first 25 numbers = 25 × 48 = 1200 Sum of last 25 numbers = 25 × 56 = 1400 Let sum of the 10 overlapping numbers be x. Then (sum of first 25) + (sum of last 25) − x = total sum 1200 + 1400 − x = 2080 2600 − x = 2080 x = 520 Average of these 10 numbers = 520 / 10 = 52.
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