Ex 3.4, 2
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :
(ii) 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?
Let Present age of Nuri = x years
& Present age of Sonu = y years
Five years ago ,
Nuri’s age = x – 5 years
Sonu’s age = y – 5 years
Given that Nuri was thrice as old as Sonu
x – 5 = 3(y – 5)
x – 5 = 3y – 15
x – 3y = –10
Ten years later,
Nuri’s age = x + 10 years
Sonu’s age = y + 10 years
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
Hence, our equations are
x – 3y = – 10 …(1)
x – 2y = 10 …(2)
Using elimination method with equation (1) & (2)
–y = –20
y = 20
Putting y = 20 in (1)
x – 3y = –10
x – 3 (20) = –10
x – 60 = –10
x = –10 + 60
x = 50
Therefore,
Present age of Nuri = x = 50 years
Present age of Sonu = y = 20 years

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 12 years. He provides courses for Maths and Science at Teachoo.