Question

The average age of a husband and a wife, who were married 4 years ago, was 25 years at the time of their marriage. The average age of the family consisting of husband, wife and a child born during that interval is 20 years, today, the child is
(a) 1 years
(b) 2 years
(c) 2.5 years
(d) 3 years

Answer 1

Hint – In this question let the present age of husband and wife be x years and y years and let the child present age be z years. The average age of a husband and his wife, who were married 4 years ago, was 25 years at the time of their marriage so the age of the husband at the time of their marriage is (x – 4) years and the age of the wife at the time of their marriage is (y – 4) years. Use the constraints of the question to formulate equations to get the value of variable z.

Complete step-by-step answer:
Let the present age of the husband be x years and the age of the wife be y years.
Now it is given that the average age of a husband and his wife, who were married 4 years ago, was 25 years at the time of their marriage.
So the age of the husband at the time of their marriage = (x – 4) years.
And the age of the wife at the time of their marriage = (y – 4) years.
So the average of them at the time of marriage is
$ \Rightarrow \dfrac{{\left( {x - 4} \right) + \left( {y - 4} \right)}}{2} = 25$, (as average of any n quantities is the ratio of sum of n quantities to the number of quantities i.e. n)
Now simplify this we have,
$ \Rightarrow x + y - 8 = 50$
$ \Rightarrow x + y = 58$..................... (1)
Now let the child present age be z years.
So the average of the family consisting 3 people is 20 years.
$ \Rightarrow \dfrac{{x + y + z}}{3} = 20$
$ \Rightarrow x + y + z = 60$
Now substitute equation (1) in the above equation we have,
$ \Rightarrow 58 + z = 60$
$ \Rightarrow z = 60 - 58 = 2$ Years.
So the present age of the child is 2 years.
Hence option (B) is the correct answer.

Note – In this question we were not concerned about the present age of wife and husband and we wish only to take out the present age of child thus, x and y are formulated rather then we have used the relation of x and y to get the value of z. Since we were landing up with 2 equations, one of which is in three variables so it was not possible to solve all three variables, as it would have required three different linear equations in 3 variables.