[Solved] 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?
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?
Solution: Let the present age of Nuri be = x years
Let the present age of Sonu be = y years
Five years ago, the age of Nuri = x – 5
Five years ago, the age Sonu = y – 5
According to the question, it is given that Nuri was thrice as old as Sonu
x – 5 = 3 (y – 5)
x – 5 = 3y – 15 ────── ①
Ten tears later age of Nuri = x + 10
Ten tears later, the age of Sonu = y + 10
Also, it is given that Nuri will be twice as old as Sonu
x + 10 = 2 (y + 10)
x + 10 = 2y + 2(10)
x + 10 = 2y + 20
x – 2y = 20 – 10
x – 2y = 10 ────── ②
Subtracting equation ① from equation ②, we get
(x – 2y) – (x – 3y) = -10 – 10
x – 2y – x + 3y = – 10 – 10
x – x – 2y + 3y = – 10 – 10
– 2y + 3y = -20
– y = – 20
y = 10
Substituting the value of y in equation ①, we get
x – 3y = -10
x – 3(20) = -10
x – 60 = -10
x = -10 + 60
x = 50
x represents the age of Nuri
y represents the age of Sonu
Hence, the present age of Nuri is 50 years, and the present age of Sonu is 20 years.
Conclusion
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu. Nuri is 50 years old, and Sonu is 20 years old.