This is one of the most important type of question of class 10th math of Chapter Pair of linear equations in two variables. How i solve this question Form the pair of linear equations for the following problems and find their solution by substitution method.(vi) 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?
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Form the pair of linear equations for the following problems and find their solution by substitution method.(vi) 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? Q.3(6)
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Let the age of Jacob and his son be x and y respectively.
According to the question,
(x + 5) = 3(y + 5)
x – 3y = 10 …………………………………….. (1)
(x – 5) = 7(y – 5)
x – 7y = -30 ………………………………………. (2)
From (1), we get x = 3y + 10 ……………………. (3)
Substituting the value of x in (2), we get
3y + 10 – 7y = -30
-4y = -40
y = 10 ………………… (4)
Substituting the value of y in (3), we get
x = 3 x 10 + 10 = 40
Hence, the present age of Jacob and his son is 40 years and 10 years, respectively.