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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

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Calculation:

Let total number of tests be a and average score of a tests be b.

Total score of a tests = ab

Average score of last (a - 10) tests = b + 1

Total score of last 10 tests = (a - 10) × (b + 1) = ab + a - 10b - 10 = ab - (10b + 10 - a)

⇒ 20 × 10 = 10b + 10 - a

⇒ 10b - a = 190   ----(1)

Average score of first (a - 10) tests = b - 1

Total score of first 10 tests = (a - 10) × (b - 1) = ab + 10 - 10b - a = ab - (a + 10b - 10)

⇒ 30 × 10 = a + 10b - 10

⇒ a + 10b = 310    ----(2)

Solving, (1) and (2)

⇒ b = 25 and a = 60

∴ Number of tests is 60.

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