Question

Ten years ago, the age of a person’s mother was three times the age of her son. Ten years hence, the mother’s age will be two times the age of her son. Their present ages are​

Answer 1

Answer:

Say,

the age of son was x and mother's age was 3x.

After ten years: Mother's age will be (3x + 10) +10

and son's age will be (x + 10) + 10.

Given that, mother's age is twice that of son after ten years.

(3x + 10): (x + 10) = 70: 30 = 7: 3.

Answer 2

$\sf \small \underline \purple{Let : - }$

$\:$

$\tt{ \implies \: the \: present \: age \: {(mother)} = x }$

$\tt{ \implies \: the \: present \: age \: {(son)} = y}$

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$\sf \small \underline \purple{To \: Find : - }$

$\tt { \implies \: the \: present \: age \: {(both)} = \: ?}$

$\sf \small \underline \purple{Solution : - }$

• Question based on linear equation with two variables so, we will solve this question by setting up equation. In the Q given that we have to find present age of mother and his son as per the given clue in question.

$\sf \small \underline{Given \: in \: clue \: (i) : - }$

• Ten years ago, the age of a person’s mother was three times the age of her son.

$\rm{ \implies \: before \: 10 \: years \: {(mother \: age)} \: = before \: 10 \: years \: {(son \: age)}}$

$\:$

$\tt{ \implies \: x - 10 = 3(y - 10)}$

$\tt {\implies \:x - 10 = 3y - 30 }$

$\tt \implies{x -3y = 30 + 10 }$

$\tt{ \implies \: x - 3y = 20 ----(l) }$

$\sf \small \underline{Given \: in \: clue \: (ii) : - }$

• Ten years hence, the mother’s age will be two times the age of her son.

$\rm{ \implies \: after \: 10 \: years \: {(mother \: age)} = after \: 10 \: years \: {(son \: age)}}$

$\tt{ \implies \: x + 10 = 2(y + 10)}$

$\tt{ \implies \: x + 10 = 2y - 20}$

$\tt{ \implies \: x - 2y = 20 - 10}$

$\tt{ \implies \: x - 2y = 10 ---- (ll)}$

• By Substracting eq (l) and (ll) we get :-

$\tt{ \implies \: x - 3y = 20}$

$\tt{ \implies \: x - 2y = 10}$

• By solving we get here :-

$\tt{ \implies \: - y = - 30}$

$\tt{ \implies \: y = 30}$

• Putting the value of y in eq (I):-

$\tt{ \implies \: x - 3y = - 20}$

$\tt{ \implies \: x - 3(30) = - 20}$

$\tt{ \implies \: x - 90 = - 20}$

$\tt{ \implies \: x = - 20 + 90}$

$\tt \green{\frak{ \implies \: x = 70}}$

$\sf \large{Hence,}$

$\sf \small \green{ \implies \: the \: present \: age \: {(mother)} = 70 \: years}$

$\sf \small \pink{ \implies \: the \: present \: age \: {(son)} = 30 \: years}$

MORE TO KNOW -

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Definition of Equation:-

→ A statement of equality which contains one or more unknown quantity or variable (literals) is called an equation.

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Definition of Linear Equation :-

→ An equation involving only linear polynomials is called a linear equation

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Definition of Solution of Linear Equation :-

→ A value of the variable which when substituted for the variable in an equation, makes LHS = RHS is said to satisfy the equation and is called a salution or root of the equation.

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