# 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? - Mathematics

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?

#### Solution

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 + 5year

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)

Putting the value of x from equation (i) we get

3y + 10 – 5 = 7y – 35

3y + 5 = 7y – 35

3y – 7y = -35 – 5

-4y = - 40

y = - 40/- 4

y = 10 year

Putting the value of y in equation first we get

x = 3 × 10 + 10

x = 40 years

Hence, Present age of Jacob = 40 years and present age of his son = 10 year

Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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Chapter 3: Pair of Linear Equations in Two Variables - Exercise 3.3 [Page 54]

#### APPEARS IN

NCERT Class 10 Maths
Chapter 3 Pair of Linear Equations in Two Variables
Exercise 3.3 | Q 6 | Page 54

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