Question

The sum of the present ages of mother and her daughter is
50 years. After 20 years mother's age will be twice her daughter's
age at that time. Find their present ages.
​

Answer 1

Answer:

The present ages of mother and her daughter are 40 years and 10 years respectively.

Step-by-step-explanation:

Let the present age of mother be x years.

And the present age of daughter be y years.

From the first condition,

x + y = 50

⇒ x = 50 - y

⇒ x = - y + 50 - - - ( 1 )

Now,

Age of mother after 20 years = ( x + 20 ) years

And age of daughter after 20 years = ( y + 20 ) years

From the second condition,

( x + 20 ) = 2 ( y + 20 )

⇒ x + 20 = 2y + 40

⇒ x - 2y = 40 - 20

⇒ x - 2y = 20

⇒ ( - y + 50 ) - 2y = 20 - - - [ From ( 1 ) ]

⇒ - y + 50 - 2y = 20

⇒ - y - 2y = 20 - 50

⇒ - 3y = - 30

⇒ 3y = 30

⇒ y = 30 ÷ 3

⇒ y = 10 years

Now, by substituting y = 10 in equation ( 1 ), we get,

x = - y + 50 - - - ( 1 )

⇒ x = - 10 + 50

⇒ x = 40 years

∴ The present ages of mother and her daughter are 40 years and 10 years respectively.

Answer 2

Question :-

• The sum of the present ages of mother and her daughter is 50 years. After 20 years mother's age will be twice her daughter's age at that time. Find their present ages.

Answer

Let

• The present age of Mother be 'x' years.

and

• The present age of daughter be 'y' years.

So,

$\bullet{ \green{ \bf \: According \: to \: statement,}}$

• The sum of present ages of mother and daughter is 50 years.

$\rm :\implies\:x + y = 50$

$\boxed{ \pink{\rm :\implies\:x = 50 - y}} - - (i)$

Now,

$\bullet{ \green{ \bf \: After \: 20 \: years}}$

• Mothers age = (x + 20) years

• Daughter age = (y + 20) years.

$\bullet{ \blue{ \bf \: According \: to \: statement,}}$

Mother age is twice the age of daughter age.

$\rm :\implies\:x + 20 = 2(y + 20)$

$\rm :\implies\:50 - y + 20 = 2y + 40 \: \: ( \because \: x \: = 50 - y)$

$\rm :\implies\:70 - y = 40 + 2y$

$\rm :\implies\:2y + y = 70 - 40$

$\rm :\implies\:3y = 30$

$\boxed{ \green{\rm :\implies\:y \: = \: 10}}$

On substituting the value of 'y' in equation (i), we get

$\rm :\implies\:x = \: 50 \: - \: 10$

$\boxed{ \green{\rm :\implies\:x \: = \: 40}}$

Hence,

• Mother present age is 40 years

and

• Daughter present age is 10 years.