Question

The sum of the ages of a daughter and mother is 56 years. After four years, the age of the mother will be three times that of the daughter. Find their present ages.

Answer 1

$\underline{ \underline \bold{Given : }}$

• The sum of the ages of a daughter and mother is 56 years.

• After four years, the age of the mother will be three times that of the daughter.

$\underline{ \underline \bold{To \: find \: out : }}$

Find their present ages ?

$\underline { \underline \bold{Solution : }}$

Let the the present daughter age be x.

Then,Mother present age = y

x + y = 56 [ Given ] .....( 1 )

⇒ y = 56 - x ......( 2 )

After four years,

★ The age of Daughter = ( x + 4 )

★ The age of mother = ( y + 4 )

According to the question,

y + 4 = 3 ( x + 4 )

⇒ y + 4 = 3x + 12

⇒ y - 3x = 12 - 4

⇒ y - 3x = 8........( 3 )

Now,

Subtracting equation ( 1 ) from ( 3 )

( x + y ) - ( y - 3x ) = 56 - 8

⇒ x + y - y + 3x = 48

⇒ x + 3x = 48

⇒ 4x = 48

⇒ x = 48/4

⇒ x = 12

Putting the value of x in Equation ( 2 )

y = 56 - x

⇒ y = 56 - 12

⇒ y = 44

Hence, the present age of daughter is 12 and mother is 44.

Answer 2

Answer:

Let the Present Age of Mother be n and of Daughter be (56 - n), as they sum up 54.

⠀

☢ Given : After four years, the age of the mother will be three times that of the daughter.

⠀

☯ $\underline{\boldsymbol{According\: to \:the\: Question :}}$

$:\implies\sf (Mother+4)=3 \times (Daughter+4)\\\\\\:\implies\sf (n+4)=3 \times [(56-n)+4]\\\\\\:\implies\sf n+4=3 \times [56-n+4]\\\\\\:\implies\sf n+4=3 \times [60-n]\\\\\\:\implies\sf n+4=180-3n\\\\\\:\implies\sf n+3n=180-4\\\\\\:\implies\sf 4n=176\\\\\\:\implies\sf n = \dfrac{176}{4}\\\\\\:\implies\sf n = 44$

⠀⠀⠀$\rule{160}{1}$

$\underline{\bigstar\:\textsf{Present Ages :}}$

$\bullet\:\:\textsf{Mother = n = \textbf{44 years}}\\\bullet\:\:\textsf{Daughter = (56 - n) = (56 - 44) = \textbf{12 years}}$