Question

Ms S Rao has two sons. At present her age is equal to the sum of the squares of their ages. Seventeen years hence, she will be twice her older son's age. Find the present ages of her sons if their age difference is 1 year.

Answer 1

Hint: In this particular type of question we first need to express the ages of both the sons as x and x + 1, then use the information given in the question to find the age of Mr Rao at present and 17 years after. Equate it with the ages of his sons after 17 years and solve the equation to get the desired answer.
Complete step-by-step solution:
According to the question , let the present ages of sons be x and x+1
Age of Ms Rao = ${x^2} + {\left( {x + 1} \right)^2}$
17 years hence ,
Rao’s age = ${x^2} + {\left( {x + 1} \right)^2} + 17$
Sons ages = x+17 and older son’s age is x+1+17 = x+18
Given that , after seventeenth years Ms s rao’s age is twice the age of older son
$
  {x^2} + {\left( {x + 1} \right)^2} + 17 = 2\left( {x + 18} \right) \\
\Rightarrow {x^2} + {x^2} + 2x + 1 + 17 = 2x + 36 \\
\Rightarrow 2{x^2} + 18 = 36 \\
\Rightarrow {x^2} = 9 \\
\Rightarrow x = 3 \\
 $
Therefore ages of his sons are 3years and 3+1=4 years

Note: Remember to recall the method of generating equations using the information given in the question. Remember to solve the equations carefully to get accurate results. Note that this question could also be done by taking the ages of his sons as x and x-1 years.