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प्रश्न
Form the pair of linear equations for the following problem 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?
उत्तर
Let present age of Jacob = x year
And present Age of his son is = y year
Five years hence,
Age of Jacob will = x + 5 year
Age of his son will = y + 5 year
Given that the age of Jacob will be three times that of his son
x + 5 = 3(y + 5)
Adding 5 both side, we get
x = 3y + 15 - 5
x = 3y + 10 ...(i)
Five years ago,
Age of Jacob will = x - 5 year
Age of his son will = y - 5 year
Jacob’s age was seven times that of his son
x – 5 = 7(y -5)
⇒ x - 5 = 7y - 35
⇒ x - 5 = 7y - 35
⇒ x - 7y = -30 ...(ii)
Putting the value of x from equation (ii) we get
x - 7y = -30
⇒ x = 7y – 30
Now on substituting the value of x in equation (i)
x - 3y = 10
⇒ 7y – 30 – 3y = 10
⇒ 4y = 10 + 30
⇒ 4y = 40
⇒ y = 10
Putting y = 10 in equation (ii)
⇒ x = 7(10) – 30
⇒ x = 70 – 30
= 40
Hence, the Present age of Jacob is 40 years and the present age of his son is 10 years.
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