NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(ii)
NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.3 Question 2(ii)
Question:
Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method :
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?
Given:
Five years ago, Nuri was thrice as old as Sonu. Ten years later, Nuri will be twice as old as Sonu.
To Find:
The present ages of Nuri and Sonu.
Formula:
Let Nuri's present age be N and Sonu's present age be S. We will form two linear equations based on the given information and solve them using the elimination method.
Solution:
Five years ago:
N - 5 = 3(S - 5) ⇒ N - 5 = 3S - 15 ⇒ N - 3S = -10 ---(1)
Ten years later:
N + 10 = 2(S + 10) ⇒ N + 10 = 2S + 20 ⇒ N - 2S = 10 ---(2)
Subtracting equation (1) from equation (2):
(N - 2S) - (N - 3S) = 10 - (-10) ⇒ N - 2S - N + 3S = 20 ⇒ S = 20
Substituting S = 20 in equation (2):
N - 2(20) = 10 ⇒ N - 40 = 10 ⇒ N = 50
Therefore, Nuri's present age (N) is 50 years and Sonu's present age (S) is 20 years.
Result:
Nuri's present age is 50 years and Sonu's present age is 20 years.
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