Question

The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age.​

Answer 1

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Let us say, present age of Rahman is x years.

Three years ago, Rehman’s age was (x – 3) years.

Five years after, his age will be (x + 5) years.

Given, the sum of the reciprocals of Rehman’s ages 3 years ago and after 5 years is equal to 1/3.

∴ 1/x-3 + 1/x-5 = 1/3

(x+5+x-3)/(x-3)(x+5) = 1/3

(2x+2)/(x-3)(x+5) = 1/3

⇒ 3(2x + 2) = (x-3)(x+5)

⇒ 6x + 6 = x2 + 2x – 15

⇒ x^2 – 4x – 21 = 0

⇒ x^2 – 7x + 3x – 21 = 0

⇒ x(x – 7) + 3(x – 7) = 0

⇒ (x – 7)(x + 3) = 0

⇒ x = 7, -3

As we know, age cannot be negative.

Therefore, Rahman’s present age is 7 years.

Answer 2

Answer:

HELLO!!❤

↓↓YOUR ANSWER↓↓

Step-by-step explanation:

♦Let Rehman's age be x.

So, three years ago

=> (x - 3) years .....(1)

And,5 years from now

=> (x + 5) years .....(2)

The sum of reciprocals of (1) and (2)

♦ 1/x - 3 + 1/ x + 5 = 1/3

♦ (x + 5) + (x - 3) / (x + 5) ( x - 3 ) = 1/3

♦ 2x + 2 / (x + 5) (x - 3) = 1/3

♦ 3(2x + 2) = (x + 5 ) (x - 3)

♦ 6x + 6 = x² - 3x + 5x - 15

♦ 6x + 6 = x² + 2x - 15 .....(3)

From eq(3)

♦ x² + 2x - 15 = 6x + 6

♦ x² +2x - 6x - 15 - 6 = 0

♦ x² - 4x - 21 = 0

♦ x² - (7 - 3)x - 21 = 0

♦ x² - 7x + 3x - 21 = 0

♦ x(x - 7) + 3(x - 7) = 0

♦ (x + 3) (x - 7) = 0

From the factors of the equation↓

1)x + 3 = 0

♦ x = -3

it is not possible because x is age.

2) x - 7 = 0

♦ x = 7

Hence,

Rehman's present age is 7 years.

HOPE IT HELPS YOU!!❤