Question

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The sum of the reciprocals of Arun's ages (in years ) 3 years ago and five years from now is 1/3 . Find his present age .

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Answer 1

The sum of the reciprocals of Arun's ages (in years ) 3 years ago and five years from now is 1/3 . Find his present age .

Good question,

Here is your perfect answer!

Let the present age be x.

So age 3 years ago = x-3 &

age 5 years from now = x+5.

According to question,

=) 1/x-3 + 1/x+5 = 1/3

=) ( x+5 + x-3) /(x+5)(x-3) = 1/3

=) (2x + 2)/ x² +2x - 15 = 1/3

=) 3(2x +2) = x² + 2x - 15

=) 6x + 6 = x² + 2x - 15

=) 0 = x² - 4x - 21

=) 0 = x² - 7x + 3x - 21

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

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

=) (x-7) = 0

=) x = 7

Hence present age is 7 years.

Answer 2

▶ Question:-

→ The sum of the reciprocals of Arun's ages ( in years ) 3 years ago and five years from now is 1/3 . Find his present age .


▶ Answer :-

→ Arun's present age is 7 years .


▶ Step-by-step explanation :-


→ Let Arun's present age be x years .

→ Arun's age 3 year ago = ( x - 3 ) years .

→ Arun's age 5 years hence = ( x + 5 ) years .


▶ Now,

$\sf \therefore \frac{1}{(x - 3)} + \frac{1}{(x + 5)} = \frac{1}{3} . \\ \\ \sf \implies \frac{(x + 5) + (x - 3)}{(x - 3)(x + 5)} = \frac{1}{3} . \\ \\ \sf \implies (x - 3)(x + 5) = 6(x + 1). \\ \\ \sf \implies {x}^{2} + 2x - 15 = 6x + 6. \\ \\ \sf \implies {x}^{2} - 4x - 21 = 0. \\ \\ \sf \implies {x}^{2} - 7x + 3x - 21 = 0. \\ \\ \sf \implies x(x - 7) + 3(x - 7) = 0. \\ \\ \sf \implies (x - 7)(x + 3) = 0. \\ \\ \sf \implies x - 7 = 0. \: \: or \: \: x + 3 = 0. \\ \\ \sf \implies x = 7 \: \: or \: \: x = - 3. \\ \\ \huge \pink{ \boxed{ \sf \implies x = 7.}} \\ \\ \bigg( \sf \because age \: cannot \: be \: negative .\: \bigg)$


✔✔ Hence, Arun's present age is 7 years ✅✅ .



THANKS.