Question

A mother said to her daughter, "At the time of your birth I was as old as you are at present”. If the mother's age is 38 years now.

Then, the daughter's age five years back was:

Answer 1

Answer:

The daughter's age five years back was 14.

Step-by-step explanation:

Assumption,

Let the present age of the daughter be 'x'.

Given,

The present age of the mother is 38.

To find,

The daughter's age, five years ago (x - 5).

Calculation,

The present age of the mother is equal to the age of the mother at her child's birth + the time gap between the birth of her daughter and the present time.

But the age of the mother at her child's birth = present age of her daughter(x)

And also the time gap between the birth of her daughter and the present time = the present age of her daughter (x)

So, our equation looks like this:

x + x = 38

⇒ x = 19

⇒ x - 5 = 14 = the daughter's age five years back.

Therefore, the daughter's age five years back was 14.

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Answer 2

Answer:

Daughter's age before 5 years= 14 years.

Step-by-step explanation:

Let the age of mother be $x$ years when daughter was born.
∴ Daughter's age= 0 years
Mother's age= $x$ years.

Now, after a period of time say $y$ years mother's age= $x+y$$= 38$ years
And daughter's age= $y$ years

Now, according to the question, mother's age at the time of daughter's birth and daughter's current age were the same
∴ $x=y$
⇒ $x+y=38$
⇒ $2y=38$
∴$y=19$

Hence, daughter's current age= 19 years.

∴ Daughter's age five years back= 19-5= 14 years.