Question

A Mother is three times as old as her daughter. 5 year later,the mother will be two and a half times as old as her daughter find the age of the daughter and that of mother in year.

Answer 1

$\huge{\blue{\underline{\underline{\rm{Solution:}}}}}$

$\textsf{Let's daughter's age be 'x'.}$

$\textsf{Mother's age be '3x'.}$

$\textsf{After 5 years their ages will be:}$

$\sf{\implies Daughter=x+5}$

$\sf{\implies Mother=3x+5}$

$\sf{\implies 2.5(x+5)=3x+5}$

$\sf{\implies 2.5x+12.5=3x+5}$

$\sf{\implies 12.5-5=3x-2.5x}$

$\sf{\implies 7.5=0.5x}$

$\sf{\implies x=\dfrac{7.5}{0.5}}$

$\sf{\implies x=15}$

$\large{\boxed{\boxed{\red{\sf{Hence,\;Daughter's\;age=15\;years}}}}}$

$\sf{\implies Mother's\;age=3x=3\times 15=45\;years}$

$\large{\boxed{\boxed{\red{\sf{Hence,\;Mother's\;age=45\;years}}}}}$

Answer 2

$\large{\red{\underline{\underline{\mathfrak{Question:}}}}}$

A Mother is three times as old as her daughter. 5 year later,the mother will be two and a half times as old as her daughter find the age of the daughter and that of mother in year.

$\large{\red{\underline{\underline{\mathfrak{Solution:}}}}}$

⇒ Let the age of Daughter = x

⇒ Age of Mother = 3x

After 5 Years,

⇒ Daughter's age = x + 5

⇒ Mother's age = 3x + 5

Now, after 5 years the mother will be two and a half times as old as her daughter. So,

⇒ 2.5(x + 5) = (3x + 5)

⇒ 2.5x + 12.5 = 3x + 5

⇒ 12.5 - 5 = 3x - 2.5x

⇒ 7.5 = 0.5 x

⇒ 7.5/0.5 = x

⇒ x = 15

So, Daughter's age = 15 years.

Mother's age = 3x

⇒ 3 × 15 = 45 years.

Hence,

⇒ Daughter's age = 15 years

⇒ Mother's age = 45 years