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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