7. 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.
Answers
Given : 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,
To Find : the total number of tests taken by him
Solution:
Let say Total Test taken = x + 10
Average Score = y
Total Score = (x + 10)y
= xy + 10y
average score increases by 1 if the first 10 tests are not considered,
=> Total score in x test = x(y + 1) = xy + x
xy + x + 10 * 20 = xy + 10y
=> x + 200 = 10y
average score decreases by 1 if the last 10 tests are not considered,
=> Total score in x test = x(y - 1) = xy - x
xy - x + 10 * 30 = xy + 10y
=> -x + 300 = 10y
x + 200 = -x + 300
=> 2x = 100
=> x = 50
x + 10 = 60
Total Test Taken = 60
Average = 25
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