Father is 5 years older than the mother and the mother’s age is now thrice the age of her daughter. The daughter is now 10 years old. What was the father’s age when the daughter was born?

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20 years

15 years

25 years

30 years

answer is C.

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Detailed Solution

Concept- We will solve this question by using the concept of mathematical modeling. The process of creating mathematical equations from given statements is known as mathematical modeling.
Let us consider that x is the age of the father, y is the age of the mother and z is the age of the daughter.
We are given that the father is 5 years older than the mother. Thus, we will write it as

The mother’s age is three times the age of the daughter. So we will write it as

It is also given that the age of the daughter is 10 years i.e.

Now we will substitute the values of equation (2) in the equation (1), we get

By substituting the value of z in equation (3), we get
Question Image

The father is now 35 years old. We will determine the father’s age at the time the daughter was born. Given that the daughter is now 10 years old, we will determine the father’s age at that time. It is determined by subtracting 10 from the current age.

As a result, the required age is 25 years.
Hence, the correct answer is option (3).

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