Problem: After finding the average of 35 scores, a student carelessly included the average with the 35 scores and found the average of these 36 numbers. The ratio of the second average to the true average was
Answer Choices:
A. 1:1
B. 35:36
C. 36:35
D. 2:1
E. None of these
Solution:
Let the 35 scores be denoted by x1​,x2​,x3​,⋯,x35​ and their average by x. Then 35xˉ=x1​+x2​+x3​⋯+x35​. The average of the 36 numbers is (x1​+x2​+x3​+⋯ +x35​+x)/36=(35x+x)/36=36x/36=x. Hence the ratio is 1:1.