Question

If twice the son's age in years is added to the father's age, the sum is 70. but if twice the father's age is added to the son's age , the sum is 95. what is the age of the son ?

Answer 1

Given

• If twice the son's age in years is added to the father's age, the sum is 70
• if twice the father's age is added to the son's age, the sum is 95.

Explanation

Let the son's age be x and Father's age be y

When twice the son's age in years is added to the father's age :-

${\pmb{\boxed{\sf{ 2x + y = 70 \ \ \ \ \ \ \ \cdots(1) }}}}$

When twice the father's age is added to the son's age :-

${\pmb{\boxed{\sf{ x + 2y = 95 \ \ \ \ \ \ \ \cdots(2) }}}}$

After Equalising both Equations (1) and (2), We have Multiply Equation(2)

with ( -2 ) as:-

$\\ \begin{cases} {\pmb{\sf{ \ \ \ \cancel{2x} + y = 70 }}} \\ {\pmb{\sf{ \cancel{ -2x } - 4y = -190 }}} \end{cases} \\ {\pmb{\boxed{\sf{ \ \ -3y = -120 }}}}$

After Calculating, We have:

${\sf{ \cancel{ -} \ 3y = \cancel{-} \ 120 }} \\ \\ \colon\implies{\sf{ \cancel{3} y = \cancel{120} }} \\ \\ \colon\implies{\sf{ y = 40 }}$

Now, By Putting value of ( y ) in any Equation to get value of ( x ) i.e. Son's age ;

$\colon\mapsto \ {\sf{ 2x + y = 70 }} \\ \\ \colon\mapsto \ {\sf{ 2x + 40 = 70 }} \\ \\ \colon\mapsto \ {\sf{ 2x = 70-40 }} \\ \\ \colon\mapsto \ {\sf{ \cancel{2} x = \cancel{30} }} \\ \\ \colon\mapsto \ {\pmb{\boxed{\sf\purple{ x = 15 }}}}$

Hence,

• Son's age will be 15 Years.
• The Age of the Father will be 40 Years.

Answer 2

Given

If twice the son's age in years is added to the father's age, the sum is 70

if twice the father's age is added to the son's age, the sum is 95.

Explanation

Let the son's age be x and Father's age be y

When twice the son's age in years is added to the father's age :-

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