Question

a boy is twice as old as his brother four hence the product of their ages (in years) will be 160 find their present ages

Answer 1

Hope it will you ....

Answer 2

His brother present age = 6 years and the boy's present age = 12 years

Step-by-step explanation:

Let the boy's present age = 2x and

His brother present age = x

To find, their present ages = ?

Four years hence,

The boy's age = (2x + 4) and

His brother present age = (x + 4)

According to question,

$(2x+4)(x+4)=160$

⇒ $2x^{2}+4x+8x+16=160$

⇒$2x^{2}+12x-144=0$

Divinding by 2, we get

⇒ $x^{2}+6x-72=0$

By factorisation method,

⇒ $x^{2}+12x-6x-72=0$

⇒ $x(x+12)-6(x+12)=0$

⇒ $(x+12)(x-6)=0$

⇒ $x+12 = 0$ or, $x-6 = 0$

⇒ x = - 12 or, x = 6 (age never be negatice)

∴ x = 6

His brother present age = 6 years

∴ The boy's present age = 2 × 6 = 12 years

Hence, his brother present age = 6 years and

the boy's present age = 2 × 6 = 12 years