Question

4. 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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MATHS

The sum of the reciprocals of Rehmans ages, (in years) 3 years ago and 5 years from now is

3

1

. Find his present age.

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ANSWER

Let the present age of Rehman =x

3 years ago Rehman’s age =(x–3) years

5 years later Rehman’s age =(x+5) years.

Now, according to the condition,

(x–3)

1

+

(x+5)

1

=

3

1

(x–3)(x+5)

(x+5+x–3)

=

3

1

(x

2

–3x+5x–15)

(2x+2)

=

3

1

x

2

+2x–15=6x+6

x

2

–4x–21=0

(x+3)(x–7)=0

Either,x+3=0 Or, x–7=0

Thus, x=7 or –3; but age cannot be negative.

Hence the present age of Rehman is 7 years

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Answer 2

Given:

• Sum of Reciprocal of Rehman age 3 years ago and 5 years from now is ⅓

To Find:

• Present age of Rehman

Solution:

Let present age of Rehman is x years.

Again,

• 3 years ago, Rehman’s age was (x – 3) years.
• 5 years after, his age will be (x + 5) years.

According to Question,

$\circ \: \: \: {\boxed{\tt{ \dfrac{1}{x-3} + \dfrac{1}{x-5} = \dfrac{1}{3} }}}$

$\colon\implies {\tt{ \dfrac{(x + 5 + x - 3)}{(x - 3)(x + 5)} = \dfrac{1}{3} }} \\ \\ \\ \colon\implies {\tt{ \dfrac{(2x + 2)}{(x - 3)(x + 5)} = \dfrac{1}{3} }} \\ \\ \\ \colon\implies {\tt{ 3(2x + 2) = (x - 3)(x + 5) }} \\ \\ \\ \colon\implies {\tt{ 6x + 6 = x^2 + 2x – 15 }} \\ \\ \\ \colon\implies {\tt{ x^2 – 4x – 21 = 0}} \\ \\ \\ \colon\implies {\tt{x^2 – 7x + 3x – 21 = 0}} \\ \\ \\ \colon\implies {\tt{ x(x – 7) + 3(x – 7) = 0 }} \\ \\ \\ \colon\implies {\tt{ (x – 7)(x + 3) = 0}} \\ \\ \\ \colon\implies {\tt\purple{ x = 7 \: and \: -3 }}$

We Know that,

• The Age can't be negative ( —ve ).

Hence,

• The Present age of the Rehman is 7 years.