Question

35. My father's age 5 years ago plus twice my age now gives 65. My age 5 years ago plus
three times my father's age now gives 130. What is my father's age?
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Answer 1

Father's present age is 40 years

Given:

Sum of father's age five years ago and twice the son's present age = 65

Sum of son's age five years ago and three times the father's present age = 130

To find: Present age of the father

Let: Present age of the father be $x$ and the present age of the son be $y$

Solution:

According to the assumptions made, if the present ages of father and son are $x \ and \ y$ respectively, then

Father's age five years ago = $x - 5$

Son's age five years ago = $y - 5$

According to the given question,

∵ $x - 5 + 2y = 65$

i.e., $x + 2y = 70$    ...(1)

also, $y - 5 + 3x = 130$

i.e., $3x + y = 135$      ...(2)

Using the elimination method to solve the equation:

Multiplying equation (2) by 2

⇒ $2(3x + y) = 2*135$

⇒ $6x + 2y = 270$   ...(3)

Subtracting equation (1) from equation (3)

⇒ $(6x + 2y) - (x + 2y ) = 270 - 70$

⇒ $6x - x + 2y - 2y = 200$

⇒ $5x = 200$

⇒ $x = \frac{200}{5} = 40$

Hence, the present age of the father is 40 years.

Project code - #SPJ3

Answer 2

Answer:

The age of father is 40

Step-by-step explanation:

Let the age of son be x and age of father be y. The according to question
$2x+y-5=65$
$2x+y=70$
and for the next equation
$3y+x-5=130$

$3y+x=135$
Then after solving the equation we get the age of son to be 15 and the age of father is 40.