Question

The sum of reciprocals of rehman's ages 3 years ago and 5 years now is 1 by 3. Find his present age.​

Answer 1

Answer:

Check the following attachment

Answer 2

Given:-

• The sum of reciprocals of Rehman's ages 3 years ago and 5 years now is 1 by 3.

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To find:-

• Find his present age.

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Solution:-

Let,

• the present age of Rehman be a.

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Here,

• Reciprocal of age of Rehman 3 years ago = 1/(a - 3) years.
• Reciprocal of age of Rehman 5 years from now = 1/(a + 5) years.

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According to the question

⇛ 1/(a - 3) + 1/(a + 5) = 1/3

⇛ (a + 5 + a - 3)/(a - 3)(a + 5) = 1/3

⇛ (2a + 2)/(a² + 2a - 15) = 1/3

⇛ 3(2a + 2) = a² + 2a - 15

⇛ 6a + 6 = a² + 2a - 15

⇛ a² + 2a - 15 - 6a - 6 = 0

⇛ a² - 4a - 21 = 0

⇛ a² - 7a + 3a - 21 = 0

⇛ a(a - 7) + 3(a - 7) = 0

⇛ (a + 3) (a - 7) = 0

⇛ (a + 3) = 0  or,  (a - 7) = 0

⇛ a = -3  or,  a = 7

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Hence,

• The present age of Rehman is 7 years.