Question

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

10 class question​

Answer 1

Given :

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

To find :

Find his present age .

Solution :

Let the present age of Rehman be 'a' years.

∴ 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.

So atq,

⇒ 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

∵ Age can't be negative. So we will neglect negative values.

∴ a = 7

∴ Present age of Rehman = 7 years.

Answer 2

Given

• Sum of reciprocals of Rehman's age 3 years ago and 5 years now is 1/3

To find

• His present age

Solution

• Let Rehman's age be x
• Then,  the reciprocal of his age 3 years ago will be = 1/(x-3)
• Then, the reciprocal of his age 5 years now will be = 1/(x+5)

Then, according to the question :-

• 1/(x-3) + 1/(x+5) = 1/3
• (2x + 2)/(x² + 2x - 15) = 1/3
• x² + 2x - 15 - 6x - 6
• x(x - 7) + 3(x - 7) = 0
• (x + 3) = 0 or (x -  7) = 0
• x = -3 or x = 7

Hence, the present age of Rehman is 7 years.