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
Explanation:
Let there be ‘n’ tests and their average be ‘x’.
By the given conditions,
When first 10 tests are not considered: ⇒ nx-200n-10 = x + 1
⇒ x = nx-200n-10 - 1 ...(1)
When last 10 tests are not considered: ⇒ nx-300n-10 = x - 1
⇒ x = nx-300n-10 + 1 ...(2)
Equating (1) and (2) ∴ nx-200n-10 - 1 = nx-300n-10 + 1
∴ nx-200n-10 - nx-300n-10 = 2
∴ 100n-10 = 2
∴ n = 60
Hence, 60.
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