Question

The sum of reciprocals of Rehman's age(in years) 3years ago and 5 years from now is 1|3.Find his present age

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Answer 1

Answer:

Let the present age of Rehman be ;

x years.

Then;

Rehman's age 3 years ago was ;

(x-3) years.

Also,

Rehman's age after 5 years will be ;

(x+5) years.

Now,

According to the question,

The sum of the reciprocals of Rehman's age 3 years ago and 5 years from now is 1/3

Thus;

=> 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 = x^2 + 5x - 3x - 15

=> x^2 + 5x - 3x - 6x - 15 - 6 = 0

=> 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 or - 3

Here,

x = -3 will be rejected, because age can never be negative.

Thus,

The appropriate value of x is 7.

Hence,

The present age of Rehman is 7 years.

Answer 2

$\bold{\underline{\underline{Answer:}}}$

Rehman's Present Age = 7 years.

$\bold{\underline{\underline{Step\:-\:by\:-\:step\:explanation:}}}$

Given :

• The sum of reciprocals of Rehman's age (in years) 3 years ago and 5 years from now is $\bold{\frac{1}{3}}$

To find :

• Rehman's present age

Solution :

Let the present age of Rehman be x years.

$\bold{Rehmans's\:age\:3\:years\:ago\:=\:x\:-\:3\:years}$

Reciprocal = $\bold{\frac{1}{x-3}}$

$\bold{Rehmans's\:age\:5\:years\:from\:now\:=\:x\:+\:5\:years}$

Reciprocal = $\bold{\frac{1}{x+5}}$

Sum of reciprocals = $\bold{\frac{1}{3}}$

$\implies$ $\bold{\frac{1}{x-3}}$ + $\bold{\frac{1}{x+5}}$ = $\bold{\frac{1}{3}}$

$\implies$ $\bold{\frac{x+5\:+\:x-3}{(x-3) (x+5)}}$ = $\bold{\frac{1}{3}}$

$\implies$ $\bold{\frac{2x\:+2}{x(x+5)-3(x+5)}}$ = $\bold{\frac{1}{3}}$

$\implies$ $\bold{\frac{2x+2}{x^2\:+\:5x\:-3x\:-\:15}}$ = $\bold{\frac{1}{3}}$

$\implies$ $\bold{\frac{2x+2}{x^2\:+\:2x\:-15}}$ = $\bold{\frac{1}{3}}$

$\implies$ $\bold{3(2x+2)\:=\:x^2+2x\:-15}$

$\implies$ $\bold{6x+6\:=\:x^2\:+2x\:-15}$

$\implies$ $\bold{x^2+2x\:-\:15=\:6x\:+6}$

$\implies$ $\bold{x^2\:+2x\:-6x\:=\:+6\:+15}$

$\implies$ $\bold{x^2\:-4x\:=\:21}$

Solving the equation via factorisation method,

$\implies$ $\bold{x^2\:-4x\:-21\:=0}$

$\implies$ $\bold{x^2\:+3x\:-\:7x\:+21\:=0}$

$\implies$ $\bold{x(x+3) -7(x+3) =\:0}$

$\implies$ $\bold{(x+3)\:\:\:(x-7) =0}$

$\implies$ $\bold{x+3=0\:\:\:OR\:\:\:x-7=0}$

$\implies$ $\bold{x=-3\:\:\:OR\:\:\:x=7}$

$\bold{x=-3\:is\:not\:acceptable}$ $\bold{Since\:age\:cannot\:be\:negative}$

•°• Rehman's present age = x = 7 years