Question

A mother is three times as old as her daughter. Six years ago, the mother's age was six tines that of her daughter. How old are they now? ​

Answer 1

Solution :

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

A mother is three times as old as her daughter. Six years ago, the mother's age was six times that of her daughter.

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

The present age of mother and daughter.

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

Let the present age of Daughter be r years.

Let the present age of Mother be m years.

So;

$\leadsto\sf{m=3r.................(1)}$

$\dag\bf{\underline{\underline{\bf{6\:years\:AgO\::}}}}}$

The age of Daughter be (r - 6) years.

The age of Mother be (m - 6) years.

Then;

$\implies\sf{(m-6)=6(r-6)}\\\\\implies\sf{m-6=6r-36}\\\\\implies\sf{3r-6=6r-36\:\:\:\:\:\:[from(1)]}\\\\\implies\sf{3r-6r=-36+6}\\\\\implies\sf{-3r=-30}\\\\\implies\sf{r=\cancel{\dfrac{-30}{-3} }}\\\\\implies\sf{\orange{r=10\:years}}$

Putting the value of r in equation (1),we get;

$\implies\sf{m=3(10)}\\\\\implies\sf{\orange{m=30\:years}}$

Thus;

$\boxed{\sf{The\:present\:age\:of\:Daughter\:is\:r=10\:years.}}}}}\\\boxed{\sf{The\:present\:age\:of\:Mother\:is\:m=30\:years.}}}}}$

Answer 2

Answer:

Given:

• A mother is three times as old as her daughter. Six years ago, the mother's age was six times that of her daughter.

Find:

• How old are they now? 

According to the question:

• Let us assume 'x' as present age of daughter and 'y' as present age of mother.

Calculations:

[ mother is three times the daughter ]

⇒ y = 3x - Equation - (1)

[ 6 years ago, mothers age was 6 times of the daughters age ]

⇒ (x - 6) years = Age of daughter.

⇒ (y - 6) years = Age of mother.

⇒ (y - 6) = 6 (x - 6)

⇒ y - 6 = 6x - 36

⇒ 3x - 6 = 6x - 36

⇒ 3x - 6x = -36 + 6

⇒ -3x = -30

⇒ x = -30/-3

⇒ x = 10

Adding the values to 'x' in equation (1):

⇒ y = 3 × 10

⇒ y = 30

Therefore, 10 years is the present age of daughter and 30 is the present age of mother.