Question

A girl is twice as her sister. Five years hence the product of their present ages is 375. Find their present ages?​

Answer 1

Answer:

$\huge{{ \pink{solve = > }}}$

Step-by-step explanation:

Given :-

Boy is Twice as old as his Brother.

Five years hence the product of their ages is 375.

Solution :-

Lets Assume That, His brother Present age is = x years.

Than, Boy Present age = 2 * x = 2x years.

A/q,

→ After 5 years His brother will be = (x + 5) years old.

→ Boy will be = (2x + 5) years old.

So,

→ (x + 5) * (2x + 5) = 375

→ 2x² + 5x + 10x + 25 = 375

→ 2x² + 15x + 25 - 375 = 0

→ 2x² + 15x - 350 = 0

Splitting The Middle Term now,

→ 2x² - 20x + 35x - 350 = 0

→ 2x(x - 10) + 35(x - 10) = 0

→ (x - 10)(2x + 35) = 0

Putting both Equal to Zero now,

→ x - 10 = 0

→ x = 10

Or,

→ 2x + 35 = 0

→ 2x = (-35)

→ x = (-35/2) ≠ Negative Value of age Not Possible.

Hence,

→ His Brother Present Age = x years = 10 years.

→ And, Boy Present Age = 2x years = 2*10 = 20 years.

So,

Boy is 20 years old now, and His brother is 10 years old now.

Answer 2

Given:

A girl is twice as her sister.

5 years hence the product of their ages is 375.

To find:

Their present ages.

Solution:

Let take the age of girl = 2x

Let take the age of sister = x

Five years hence,

(2x + 5) (x +5) = 0

${2x}^{2} + 10x + 5x + 25 = 375$

${2x}^{2} + 15x + 25 - 375 = 0$

${2x}^{2} + 15x - 350 = 0$

Splitting the middle terms

${2x}^{2} - 20x + 35x - 350 = 0$

$2x(x - 10) \: 35(x - 10) = 0$

$(x - 10)(2x + 35) = 0$

Solving x

$x - 10 = 0 \: \: \: \pink{or} \: 2x + 35 = 0$

$x = 0 + 10 \: \: \pink{or} \: 2x = 0 - 35$

$x = 10 \: \: \pink{or} \: 2x = - 35$

$x = 10 \: \: or \: x = \frac{ - 35}{2}$

Negative value is not accepted.

Therefore x = 10.

Then

2x = 2(10) = 20

x = 10

The girl age = 20

her sister age = 10