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 ?

byAmlesh Mahato •November 24, 2021

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Solution:

⇒ Given

⇒ Let the present age of Rehman be x

⇒ Age of Rehman 3 years ago = x - 3

⇒ Reciprocal = 1/(x-3)

⇒ Age of Rehman after 5 years = x + 5

⇒ Reciprocal = 1/(x+5)

A/Q

$The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age ?,Chapter-4,Exercise-4.3,Math- Class 10,$

$\large \Rightarrow \frac{x+5+x-3}{\left ( x-3 \right )\left ( x+5 \right )}=\frac{1}{3}$

$The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age ?,Chapter-4,Exercise-4.3,Math- Class 10,$

$\large \Rightarrow 3\left ( 2x+2 \right )=\left ( x-3 \right )\left ( x+5 \right )$

$\large \Rightarrow 6x+6=x^{2}+5x-3x-15$

$\large \Rightarrow 6x+6=x^{2}+2x-15$

$\large \Rightarrow x^{2}+2x-15-6x-6=0$

$The sum of the reciprocals of Rehman’s ages, (in years) 3 years ago and 5 years from now is 1/3. Find his present age ?,Chapter-4,Exercise-4.3,Math- Class 10,$