Question

the sum of the reciprocal of rehmans ages 3 years ago and 5 years from now os 1/3.find his present age​

Answer 1

$\bf{\huge{\underline{\boxed{\tt{\blue{Answer:}}}}}}$

Given :-

• the sum of the reciprocal of rehmans ages 3 years ago and 5 years from now is $\bf\large\frac{1}{3}$

To find :-

• Rehman's present age.

Solution :-

Let Rehman's present age be x years.

Rehman's age three years ago = x - 3 years

Reciprocal of Rehman's ages 3 years ago = $\bf\large\frac{1}{x -3}$

Rehman's age five years from now = x + 5

Reciprocal of Rehman's age 5 years from now = $\bf\large\frac{1}{x + 5}$

Sum of reciprocals = $\bf\large\frac{1}{3}$

Let's start with the solution!

$\bf\large\frac{1}{x - 3}$ + $\bf\large\frac{1}{x + 5}$ = $\bf\large\frac{1}{3}$

Cross multiplying and multiplying,

$\bf\large\frac{x + 5 + x - 3}{(x-3) (x + 5)}$ = $\bf\large\frac{1}{3}$

$\bf\large\frac{2x + 2}{x(x +5) -3(x +5)}$ = $\bf\large\frac{1}{3}$

$\bf\large\frac{2x+ 2}{x^2 + 5x - 3x - 15}$ = $\bf\large\frac{1}{3}$

$\bf\large\frac{2x + 2}{x^2 +2x - 15}$ = $\bf\large\frac{1}{3}$

Cross multiplying,

3 ( 2x + 2) = x² + 2x - 15

6x + 6 = x² + 2x - 15

x² + 2x - 15 = 6x + 6

x² + 2x - 6x = 6 + 15

x² - 4x = 21

x² - 4x - 21 = 0

Use factorisation method,

x² - 7x + 3x - 21 = 0

x ( x - 7 ) 3 ( x - 7) = 0

( x - 7 ) (x + 3) = 0

x - 7 = 0 OR x + 3 = 0

x = 7 OR x = - 3

Age cannot be negative.

•°• x = - 3 is not acceptable.

•°• Present age of Rehman = 7 years

$\bf{\huge{\underline{\boxed{\rm{\red{Verification:}}}}}}$

Present age of Rehman = 7 years

Three years ago Rehman's age = 7 - 3 = 4 years

Reciprocal = $\bf\large\frac{1}{4}$

Five years from now Rehman's age = 7 + 5 = 12 years.

Reciprocal = $\bf\large\frac{1}{12}$

Sum of reciprocal =$\bf\large\frac{1}{3}$

Let's check whether we got our answer right or wrong.

$\bf\large\frac{1}{4}$ + $\bf\large\frac{1}{12}$ = $\bf\large\frac{1}{3}$

Cross multiply and multiply the terms,

$\bf\large\frac{12 + 4}{( 12) (4)}$ = $\bf\large\frac{1}{3}$

$\bf\large\frac{16}{48}$ = $\bf\large\frac{1}{3}$

On dividing on LHS by 16,

$\bf\large\frac{1}{3}$ = $\bf\large\frac{1}{3}$

LHS = RHS.

Hence the answer is right.

Answer 2

Answer:

Please refer the attachment dear