Question

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

Hint: Suppose present age of Nuri and Sonu as two variables. Now, apply the given conditions to form two equations. Now, try to solve them to get values of variables which represent present ages of Nuri and Sonu.

Let us suppose, present age of Nuri be ‘x’ years and present age of Sonu be ‘y’ years.
Now, it is given that five years ago, Nuri was thrice old as Sonu. Hence,
Five years ago,
Nuri’s age = x-5 years
Sonu’s age = y-5 years
And relation between ages can be given as
Nuri’s age = 3$\times$sonu’s age or
x-5 = 3(y-5)
x-5 = 3y-15
x-3y+10 = 0 ………..(i)
Another relation is given in the problem that ten years later, Nuri is twice as old as Sonu.
So, ten years ago,
Nuri’s Age = x+10
Sonu’s Age = y+10
And relation between ages can be written as
x+10 = 2(y+10)
x+10 = 2y+20
x-2y-10 = 0 …………..(ii)
Now we can solve the equation (i) and (ii) to get values of x and ‘y’ or present ages of Nuri and Sonu.
Value of ‘x’ from equation (i) be
x = 3y-10 ……….(iii)
Putting value of ‘x’ from equation (iii) in equation (ii) we get,
3y-10-2y-10 = 0
y = 20
Now, from equation (iii) value of ’x’ can be given as,
x= 3(20)-10
x = 50

Hence, the present ages of Nuri and Sonu are 50 years and 20 years respectively.

Note: One can verify the relation between ages of Nuri and Sonu by the given conditions. If answers are not satisfying the given conditions, then your solution is incorrect. One can go wrong while writing the relation between ages when it was five years ago and ten years later as well. He or she may write both equations as 3(x-5) = (y-5) or 2(x+10) = y+10 which are wrong. Hence, we need to take care while converting word problems to mathematical equations which is the key point of these kind of questions.