Question

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?

Answer 1

Hint: We can take the present age of the father, mother and daughter as 3 variables. Then we can form 3 equations using the details given in the question. Then we can solve for the variables to obtain the present age of the father. We get the required age of the father by subtracting the age of the daughter from the father’s present age.

Complete step-by-step answer:
Let x be the age of the father, y be the age of the mother and z be the age of the daughter.
It is given that the father is 5 years older than the mother. So, we can write
$x = y + 5$ … (1)
The mother’s age is thrice the age of the daughter. So, we can write
$ \Rightarrow y = 3z$ .. (2)
It is given that the age of the daughter is 10 years.
$ \Rightarrow z = 10$… (3)
We can substitute the value of equation (2) in equation (1). So, we get
$ \Rightarrow x = 3z + 5$
On substituting value of equation (3), we get
$ \Rightarrow x = 3 \times 10 + 5$
On doing further calculations, we get
$ \Rightarrow x = 30 + 5 = 35$
So, the present age of the father is 35 years. We need to find the age of the father when the daughter was born. As the daughter is 10 years old now, we need to find the age of the father 10 years ago. It is given by subtracting 10 from the present age.
$ \Rightarrow 35 - 10 = 25$
Therefore, the required age is 25 years.
So, the correct answer is option C .

Note: We used the concept of mathematical modelling to solve this problem. Mathematical modelling is the method of forming mathematical equations from given statements. In this problem we took the present ages of the persons as the variable. We must make sure that all the variables used are taken as the age is in the same time period. We have 3 equations and 3 variables. So, we can easily solve for all the variables. As we are asked only the age of the father, it is not necessary that we solve for all the variables.