Question

The sum of the ages of two children is 30 years five years ago the product of their ages was 120 years is it possible for the sum of their present age to be 30

Answer 1

Given :-

• The sum of the ages of two children is 30 years .
• five years ago the product of their ages was 120.

To verify :-

• is it possible for the sum of their present age to be 30 ?

Solution :-

Let us assume that, the present age of one children is x years.

Than,

→ Present age of second children = (30 - x) years.

Now,

→ 5 years ago , first children was = (x - 5) years old.

→ 5 years ago, second children was = (30 - x) - 5 = (25 - x) years old.

Given that, product of both ages was 120 years.

So,

→ (x - 5)(25 - x) = 120

→ 25x - x² - 125 + 5x = 120

→ - x² + 30x - 125 = 120

→ x² - 30x + 125 + 120 = 0

→ x² - 30x + 245 = 0

Now, we know that, in any quadratic equation, A•x^2 + B•x + C = 0 , discriminant is given by :-

• D = B^2 - 4•A•C
• If D = 0 , then the given quadratic equation has real and equal roots.
• If D > 0 , then the given quadratic equation has real and distinct roots.
• If D < 0 , then the given quadratic equation has unreal (imaginary) roots...

comparing the given equation x² - 30x + 245 = 0 with A•x^2 + B•x + C = 0 we get ,

• A = 1
• B = (-30)
• C = 245 .

So,

→ D = B^2 - 4•A•C

→ D = (-30)² - 4 * 1 * 245

→ D = 900 - 980

→ D = (-80)

As, we can see

→ (-80) < 0.

→ D < 0.

Therefore, we can conclude that, value of x will be a unreal number.

Since age in years cant be a imaginary number .

Hence, it is NOT possible for the sum of their present age to be 30 years .