radha was asked to find the average of N consecutive natural numbers starting from 1. By mistake,he added a number twice but he didn't notice it.As a result, he obtained a wrong number of 45 11/18.Find the number she added twice.
Answers
Given : the average of N consecutive natural numbers starting from 1
By mistake, added a number twice
a wrong number of 45 11/18
To Find : number she added twice.
Solution:
Consecutive numbers added = N
Sum of first N numbers = N(N + 1)/2
Average = (N + 1)/2
added a number twice
Let say x
The average increased because of x is between 0 and 1
as 1 ≤ x ≤ N
Average obtained = 45 11/18
Hence Correct average could be 45 or 45.5
Case 1 : average 45
= (N + 1)/2 = 45 => N = 89
=> Sum = 89 * 45 = 4005
(45 11/18) * 89 = Does not give integer
Case 1 : average 45.5
=> N = 90
Sum = 90 * 45.5 = 4095
(45 11/18) * 90 = 4,105
She added 4105 - 4095 = 10 twice
she added 10 twice.
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I hope it helps all.
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