A CAT aspirant appears for a certain number of tests. His average score increases by 1 if the first 10 tests are not considered, and decreases by 1 if the last 10 tests are not considered. If his average scores for the first 10 and the last 10 tests are 20 and 30, respectively, then the total number of tests taken by him is
Started 3 months ago by Shashank in
Explanatory Answer
Let there be 'n' tests and the Overall Average score be k
Average (n) = k => Total marks = nk
So, when we ignore the first 10 questions,
Average (n-10) = k+1
Similarly, if we ignore the last 10 questions,
Average (first (n-10)) = k-1
It is given that when the first 10 tests are not considered, the overall average increases by 1
(Each question carries 20 marks)
Total marks – 20×10 = (k+1) (n-10)
kn – 200 = (k+1) (n-10) ---(1)
Similarly, If the last 10 tests are not considered, the overall average decreases by 1 (Each
question carries 30 marks)
kn - 300 = (k-1) (n-10) ---(2)
Solving (1) and (2), we get
kn - 200 = (k+1) (n-10)
(-) kn - 300 = (k-1) (n-10)
-------------------------------------
100 = 2(n-10)
50 = n-10
n = 60 questions
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