Question

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

Answer 1

AnswEr :

$\bf{\pink{\underline{\underline{\bf{Given\::}}}}}$

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

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

Their present ages.

$\bf{\purple{\underline{\underline{\bf{Explanation\::}}}}}$

Let the present age of sister be r

Let the present age of girl be 2r

$\underbrace{\bf{After\:5\:years\::}}}}}$

$\leadsto\sf{The\:age\:of\:sister\:=(r+5)\:years}\\\\\leadsto\sf{The\:age\:of\:girl\:=(2r+5)\:years}}$

$\bf{\red{\underline{\underline{\tt{A.T.Q\::}}}}}$

$\dashrightarrow\tt{(r+5)(2r+5)=375}\\\\\\\dashrightarrow\tt{2r^{2} +10r+5r+25=375}\\\\\\\dashrightarrow\tt{2r^{2} +15r+25=375}\\\\\\\dashrightarrow\tt{2r^{2} +15r=375-25}\\\\\\\dashrightarrow\tt{2r^{2} +15r=350}\\\\\\\dashrightarrow\tt{2r^{2} +15r-350=0}\\\\\\\dashrightarrow\tt{2r^{2} -20r+35r-350=0\:\:\:\:\big[factorise\big]}\\\\\\\dashrightarrow\tt{2r(r-10)+35(r-10)=0}\\\\\\\dashrightarrow\tt{(r-10)(2r+35)=0}\\\\\\\dashrightarrow\tt{r-10=0\:\:Or\:\:2r+35=0}$

$\dashrightarrow\tt{\red{r=10\:\:\:\:Or\:\:\:\:r=-\dfrac{35}{2} }}$

We know that negative value isn't acceptable.

Thus,

$\underbrace{\sf{The\:present\:age\:of\:sister\:=r=10\:years.}}}}}\\\\\underbrace{\sf{The\:present\:age\:of\:girl\:=2r=2*10=20\:years.}}}}}$

Answer 2

Given :-

• Girl is Twice as old as her sister.
• Five years hence the product of their ages is 375.

Solution :-

Lets Assume That, Her Sister Present age is = x years.

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

A/q,

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

→ Her Sister 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,

→ Her sister Present Age = x years = 10 years.

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

So, Girl is 20 years old now, and her sister is 10 years old now.