Question

The sum of the reciprocals of Rehmans age,3years ago and 5years from now is 1/3.Find his present age.​

Answer 1

Answer:

The sum of the reciprocals of Rehmans ages, (in years) 3 years ago and 5 years from now is 31. Find his present age. 5 years later Rehman's age =(x+5) years. Thus, x=7 or –3; but age cannot be negative.

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Answer 2

Answer

Given,

• Sum of reciprocal of Rehman's age 3 yr ago and 5 yr from now is 1/3

To find,

• Present age of Rehman

Solution ,

Let Rehman's present age be 'x'

Hence,

3 yrs ago his age was:

⇛ x - 3

5 yrs form now his age will be:

⇛ x + 5

According to the question :

⇛ $\rm \frac { 1 } { x - 3 } + \frac { 1 } { x + 5 } = \frac { 1 } { 3 }$

Taking LCM = (x - 3)(x + 5)

⇛ $\rm \frac { (x + 5) + (x - 3) } {(x - 3)(x + 5) } = \frac { 1 } { 3 }$

⇛ $\rm \frac { 2x + 2 } { x^2 + 5x - 3x - 15 } = \frac { 1 } { 3 }$

⇛ $\rm \frac { 2x + 2 } { x^2 + 2x - 15 } = \frac { 1 } { 3 }$

Cross multiplying

⇛ 6x + 6 = x² + 2x - 15

⇛ x² - 4x - 21 = 0

Here we got a quadratic equation.Let us solve it by splitting the middle term method.

⇛ x² + 3x - 7x - 21

⇛ x(x + 3) -7(x + 3)

⇛ (x + 3)(x - 7)

• x = -3
• x = 7

Age cannot be negative hence x = 7

So, we got that Rehman's present age is 7 yrs