Question

Mrs. Robert is 3 times older than her son. The sum of their ages is 48 years. How old was Mrs. Robert when her son was born ?

Answer 1

Hint:n this question starts with finding the present age of Mrs. Robert and her son. To find their present ages use the given two conditions. After this step, to find the age of Mrs. Robert when her son was born, consider the age of her son’s age when he was born as zero and proceed with the solution.

Complete step by step answer:
We have to find how old Mrs. Robert was when her son was born. To find this we will start with assuming the present age of Mrs. Robert as x and present age of her son as y. According to the first given condition, Mrs. Robert is 3 times older as her son. This implies that the age of Mrs. Robert is three times that of her son’s age.We can write it mathematically as,
$x = 3y - - - \left( 1 \right)$
The second condition mentioned in the question is that the sum of the present ages is 48.We can write this condition mathematically as well in the form,
$x + y = 48 - - - \left( 2 \right)$
Substituting the value of equation (1) in equation (2) we get
$3y + y = 48$

Solving this equation further we get,
$4y = 48 \\
\Rightarrow y = 12 $
Hence from the above equation we get that the present age of the son is 12 years.
Substituting the value of y in (1) we get
$x = 3y \\
\Rightarrow x = 12 \times 3 \\
\Rightarrow x = 36 $
Hence the present age of Mrs. Roberts is 36 years old. In the question we have been asked the age of Mrs. Roberts when her son was born. That is when her son’s age was 0, Mrs. Roberts age would be her present age minus hers son’s age.That is 36-12=24

Hence Mrs. Roberts was 24 years old when her son was born.

Note:Thus kind of questions about relations are easy to solve when written in form of equations. Always try to write the condition given in the questions in the form of mathematical equations. Also finding the present value first and then finding the past or future age value is the trick used to solve this type of question.