The average of 6 values is 12. A number is added and the average increases by 1. Find the number added.
Explanation:
Let x be the value of number added.
Given, (6 × 12 + x)/7 = 13
⇒ 72 + x = 91
⇒ x = 19.
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 increases by 1 ⇒ the total increase in all numbers = 7 × 1 = 7.
This means that the number added was 7 more than the old average.
⇒ x = 12 + 7 = 19.
Hence, 19.
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