Question

Rahul is twice as old as rohit. Four year hence the product of their ages will be 160 find their present ages

Answer 1

let rohit's present age be x.

so, rahul's age us 2x

now, 4 years hence, they'll each grow 4 years older,

So, (x+4)(2x+4)=160

2x^2+8x+4x+16=160

2x^2+12x+16=160

x^2+6x+8=80

x^2+6x-72=0

x^2+12x-6x-72=0

x(x+12)-6(x+12)=0

(x-6)(x+12)=0

x-6=0 or x+12=0

x=6 x=-12

since, age can't be negative, therefore, rohit's age is 6 and thus, rahul's age is 2×6=12

I hope my answer helps

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Answer 2

$\underline{\underline{\bold{Solution:}}}$

Let the age of Rohit be x years .

So , the age of Rahul = 2 x years.

After 4 years,

• The age of Rohit = (x+4) years.

• The age of Rahul = (2x+4) years.

According to question,

The product of their ages will be = 160.

$\implies\tt{(x+4)(2x+4)=160}\\\\\\\implies\tt{2x^2+4x+8x+16=160}\\\\\\\implies\tt{2x^2+12x+16=160}\\\\\\\implies\tt{2x^2+12x+16-160=0}\\\\\\\implies\tt{2x^2+12x-144=0}\\\\\\\implies\tt{2(x^2+6x-72)=0}\\\\\\\implies\tt{x^2+6x-72=0}\\\\\\\implies\tt{x^2+12x-6x-72=0}\\\\\\\implies\tt{x(x+12)-6(x+12)=0}\\\\\\\implies\tt{(x+12)(x-6)=0}\\\\\\\implies\tt{x=-12\:or\:6.}\\\\\\\underline{\textbf{Possible value of x = 6.}}$

$\boxed{\boxed{\textbf{The age of Rohit and Rahul is 6 years and 12 years respectively.}}}$