NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(vi)
NCERT Class X Chapter 3: Pair of Linear Equations In Two Variables Exercise 3.2 Question 3(vi)
Question:
Form the pair of linear equations for the following problems and find their solution by substitution method.
Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Given:
Let Jacob's present age be J years and his son's present age be S years.
Five years hence, Jacob's age will be three times that of his son.
Five years ago, Jacob’s age was seven times that of his son.
To Find:
Their present ages (J and S).
Formula:
Formulate two linear equations based on the given information and solve them using the substitution method.
Solution:
Five years hence, Jacob's age will be three times that of his son:
J + 5 = 3(S + 5) ⇒ J + 5 = 3S + 15 ⇒ J = 3S + 10 ...(1)
Five years ago, Jacob’s age was seven times that of his son:
J - 5 = 7(S - 5) ⇒ J - 5 = 7S - 35 ⇒ J = 7S - 30 ...(2)
Substitute (1) in (2):
3S + 10 = 7S - 30 ⇒ 4S = 40 ⇒ S = 10
Substitute S = 10 in (1):
J = 3(10) + 10 ⇒ J = 40
Result:
Jacob's present age (J) = 40 years
His son's present age (S) = 10 years
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