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# Represent the following situations in the form of quadratic equations:

Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360. We would like to find Rohan’s present age.

Given :

Rohan’s mother is 26 years older than him. The product of their ages (in years) 3 years from now will be 360.

To find :

We have to find Rohan’s present age.

Solution :

Let the present age of Rohan be $x$.

This implies,

The age of the mother $= x+26$

Age of the Rohan after 3 years $= x+3$

Age of the mother after 3 years $=(x+26)+3=x+29$.

Therefore,

$(x+3)(x+29) = 360$

$x(x+29)+3(x+29) = 360$

$x^2+29x+3x+87 = 360$

$x^2+32x+87-360 = 0$

$x^2+39x-7x-273=0$

$x(x+39)-7(x+39)=0$

$(x+39)(x-7)=0$

$x+39=0$ or $x-7=0$

$x=7$ or $x=-39$ which is not possible

The present age of Rohan is $7$ years.

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