Question

Five years from now, the sum of the ages of a women and her daughter will be 40 years. The difference in their present age is 24 years. How old is her Daughter now?

Answer 1

Answer:

Her daughter is 3 years old now.

Step-by-step explanation:

Given:

Five years from now, the sum of the ages of a women and her daughter will be 40 years.

The difference in their present age is 24 years.

Now, to find how old is her daughter now.

Let the age of daughter be $x\ years$.

And the age of mother be $y\ years$.

According to question:

$(x+5)+(y+5)=40$

⇒ $x+y+10=40$

Subtracting both sides by 10 we get:

⇒ $x+y=30$

⇒ $x=30-y$............( 1 )

Now, as given in question:

The difference in their present ages is 24 years.

$x-y=24$

Putting the equation ( 1 ) in the place of $x$ we get:

⇒ $(30-y)-y=24$

⇒ $30-2y=24$

Moving variable on one side and the numbers on the other:

⇒ $30+24=2y$

⇒ $54=2y$

Dividing both sides by 2 we get:

⇒ $27=y$

So, the age of the mother is 27 years.

Now, putting the value of  $y$ in equation( 1 ) we get:

$x=30-27$

⇒ $x=3$

The age of daughter is 3 years.

Therefore, her daughter is 3 years old now.