Question

Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. How old are Nuri and Sonu?

Answer 1

Hint: In this question assume age of Nuri to be any variable and age of Sonu be any other variable then according to the given equation construct the linear equations so, use these concepts to reach the solution of the question.

Complete step-by-step answer:

Let the present age of Nuri be x years.
And the present age Sonu is by years.
Now it is given that five years ago, Nuri was thrice old as Sonu.
Now construct the linear equation according to given information we have,
Age of Nuri five years ago is equal to 3 multiplied by the age of Sonu five years ago.
$ \Rightarrow x - 5 = 3\left( {y - 5} \right)$…………………….. (1)
Now it is also given that 10 years later Nuri will be twice as old as Sonu.
Now again construct the linear equation according to given information we have,
$ \Rightarrow \left( {x + 10} \right) = 2\left( {y + 10} \right)$…………………….. (2)
Now from equation (1) the value of x is
$ \Rightarrow x = 3\left( {y - 5} \right) + 5 = 3y - 10$
Now put the value of x from equation (1) in equation (2) we have,
$ \Rightarrow \left( {3y - 10 + 10} \right) = 2\left( {y + 10} \right)$
Now simplify the above equation we have,
$ \Rightarrow 3y - 2y = 20$
$ \Rightarrow y = 20$ years.
Now put the value of y in equation (1) we have,
$ \Rightarrow x - 5 = 3\left( {20 - 5} \right)$
Now simplify the above equation we have,
$ \Rightarrow x = 45 + 5 = 50$ years.
So, the present age of Nuri is 50 years and the present age Sonu is 20 years.
So, this is the required answer.

Note: In such types of questions first of all let the age of Nuri and Sonu be x and y years respectively, then according to given information construct the linear equations as above, then simplify these equations using any method and calculate the values of x and y which is the required answer of the question.