The Marks obtained by Rahul in first four tests in Mathematics subjects are increased in
Arithmetic Progression. If the sum of the marks obtained by him in second and fourth test is
22 and the product of marks got by him in first and fourth tests is 85, how many marks did
Rahul scored in each test ?
Answers
The marks obtained by Rahul in each test are 5, 9, 13 and 17
Given:
The Marks obtained by Rahul in first four tests in Mathematics subjects are increased in Arithmetic Progression.
The sum of the marks obtained by him in second and fourth test = 22
The product of marks got by him in first and fourth tests = 85
To find:
How many marks did Rahul scored in each test ?
Solution:
Let (a-3d), (a-d), (a+d), (a+3d) are be the scores obtained by Rahul in 4 tests with common difference 2d
Given The sum of the marks obtained in 2nd and 4th test = 22
⇒ (a-d) + (a+3d) = 22
⇒ 2a+2d) = 22
⇒ 2a + 2d = 22
⇒ 2(a+d) = 22
⇒ (a+d) = 11 ----(1)
The product of marks got in 1st and 4th tests = 85
⇒ (a-3d)(a+3d) = 85
⇒ (a² - 9d² = 85
⇒ 121 - 9d² = 85
⇒ 9d² = 36
⇒ d² = 4
⇒ d² = 2²
⇒ d = 2
The marks obtained,
a-3(2) = 11 - 6 = 5
a - d = 11 - 2 = 9
a + d = 11 + 2 = 13
a+3d = 11 + 3(2) = 11 + 6 = 17
The marks obtained by Rahul in each test are 5, 9, 13 and 17
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