Question

the sum of reciprocal of Tehran's age ( in years)3 years ago and 5years from now is 1/3. FIND his present age

Answer 1

Answer:

Let his present age be x.

Age three years ago = x - 3   ...( 1 )

Age 5 years hence = x + 5   ...( 2 )

Sum of Reciprocals of ( 1 ) and ( 2 ) is 1 / 3.

To find his present age = ?

Substituting the values we get,

$\\\implies \dfrac{1}{x-3} + \dfrac{1}{x + 5 } = \dfrac{1}{3} \\\\\text{ Taking LCM we get,} \\\\\implies \dfrac{ x + 5 + x - 3 }{ ( x + 5 )( x - 3 )} = \dfrac{1}{3} \\\\\\\implies \dfrac{2x + 2 }{x^2 - 3x + 5x - 15 } = \dfrac{1}{3}\\\\\implies \dfrac{2x+2}{x^2 + 2x - 15} = \dfrac{1}{3}\\\\\text{ Cross multiplying we get,} \\\\\implies 3 ( 2x + 2 ) = 1 ( x^2 + 2x - 15 )\\\\\implies 6x + 6 = x^2 + 2x - 15 \\\\\implies x^2 + 2x - 6x - 15 - 6 = 0\\\\\implies x^2 - 4x - 21 = 0$

$\implies x^2 - 7x + 3x - 21 = 0\\\\\implies x ( x - 7 ) + 3 ( x - 7 ) = 0\\\\\implies ( x - 7 ) ( x + 3 ) = 0\\\\\implies x = 7, -3$

Age cannot be negative. Hence -3 is ignored.

Hence the present age of Tehran is 7 years.

Answer 2

Answer:

Please refer the attachment dear