The average of 6 values is 12. A number is added and the average decreases by 1. Find the number added.
Explanation:
Let x be the value of number added.
Given, (6 × 12 + x)/7 = 11
⇒ 72 + x = 77
⇒ x = 5.
Alternately,
Had the number added been same as average (i.e. 12), the average of now 7 numbers would not have changed.
Since average of now 7 numbers decreases by 1 ⇒ the total decrease of all numbers = 7 × 1 = 7.
This means that the number added was 7 less than the old average.
⇒ x = 12 - 7 = 5.
Hence, 5.
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