Question

3. If we double the age of a man and subtract it from his father's age we get 15. If we double the father's age and add it to the son's age we get 105. Find their present ages.
Ans. ​

Answer 1

$★ {\pmb{\underline{\sf{Required \ Solution ... }}}}$

Let the age of the man be x and age of the man's Father be y.

★ Condition 1

If we double the age of a man and subtract it from his father's age,

$\colon\implies{\tt{ y - 2x = 15 }}$

★ Condition 2

If we double the father's age and add it to the man's age,

$\colon\implies{\tt{ 2y + x = 105 }}$

» By Applying Elimination Method, We got that,

$\colon\implies{\tt{ x = 14 \ Years }}$

Now Finally, By Putting value of x in any Equation to get the value of y as:

$\colon\Rightarrow{\tt{ y - 2 \times 14 = 15 }} \\ \\ \colon\Rightarrow{\tt{ y - 28 = 15 }} \\ \\ \colon\Rightarrow{\tt{ y = 15 + 28 }} \\ \\ \colon\Rightarrow{\tt{y = 43 \ Years }}$

Hence,

The Present age of the man is 14 years and age of the man's Father is 43 years.

Answer 2

Answer:

Currently, if father's age is x and son's age is y,

then given, x+2y=70 --- (1)

2x+y=95 --- (2)

Multiplying equation (1) with 2 we get, 2x+4y=140 --- (3)

Subtracting equation (2) from (3), we get 3y=45⇒y=15

Substituting y=15 in the equation (2), we get

2x+15=95⇒x=40

Hence, the father is 40 years old and the son is 15 years old.