Question

sum of the present age of mother and daughter is 40 years. Find the sum of their age before 10?

Answer 1

$\huge{ \underline{ \overline{ \mid{ \mathfrak{ \purple{ \: \: SOLUTION \: \: } \mid}}}}}$

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \text{The sum of present ages of mother } \\ \text{and daughter = 40 years} \\ \\ \underline {\mathfrak{ \: \: To \: \: find : \mapsto}} \\ \\ \text{Sum of the ages of mother and } \\ \text{daughter before 10 years = ?}$

$\underline{ \mathfrak{ \: \: Suppose, \: \: }} \\ \\ \text{Present age of the mother = \red{x} \: years} \\ \\ \text{Present age of the daughter = \red{ y } \: years.}$

$\underline{ \bold{ \: A.T.Q., \: }} \\ \\ \text{Present age of the mother + Present} \\ \: \: \: \: \: \: \: \: \: \: \: \: \text{ age of the daughter = 40} \\ \\ \implies \: \: \text{x + y = 40 \: \: - - - - - - - - - > (1)}$

$\mathfrak{ \: Now, \: } \\ \\ \underline{ \text{ \: Before \: 10 \: years \: }} \\ \\ \text{The age of the mother will be (x-10) years} \\ \\ \tt{And,} \\ \\ \text{The age of the daughter will be (y-10) years.} \\ \\ \tt{ \therefore \: \: Sum \: \: of \: \: their \: \: ages \: \: will \: \: be} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{ =(x -10 ) + (y -10)} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{ = x -10 + y - 10} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{= (x + y) - 10 - 10 } \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{= 40 - 20 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [From \: (1)]} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{= 20 }$

$\therefore \sf{Sum \: \: of \: \: the \: \: ages \: \: of \: \: mother \: \: and } \\ \sf{daughter \: \: before \: \: 10\: \: years = \red{20 \: \: years}}$

Answer 2

$\huge\underline\textsf{Question:- }$

$\small\textsf{sum of the present age of mother}\\\sf{ and daughter is 40 years. Find the }\\\sf{sum of their age before 10?} }$

Ans $\small\textbf{\red{[20 years]} }$

$\sf\blue{Given}\begin{cases}\sf\red{Sum\: of \:the \:present\: age } \\ \sf\green{of \:mother\: and} \\\sf\blue{Daughter=40year}\end{cases}$

$\huge\underline\textsf{To Find :- }$

$\small\underline{\underline{\texttt{\purple{the \:sum \:of \:their\: age \:before \:10?}}}}$

$\large\underline\textsf{Suppose:- }$

$\small\textbf{Present\: age \:of\: the\: mother = \red{A\:year}}$

$\small\textbf{Present \:age\: of \:the \:daughter = \red{B \:year }}$

$\huge\underline\textsf{Explantion:- }$

$\boxed{\bf mother \: age + daughter \: age}$

$\small\underline\textsf{Identiti Used:- }$

$\boxed{\sf(a + b) {}^{2} = a {}^{2} + 2ab + b2 {}^{2}}$

$\small\underline\textsf{Now, }$

$\small\underline\textsf{The age of the mother will be (\red{A-10}) years }$

$\small\underline\textsf{The age of the daughter will be (\red{B-10}) years. }$

$\huge\underline{\underline\textsf{\:\:\:\:\:\:\:\:sum of the ages}}$

$\implies\sf (a - 10) + (b - 10)$

$\implies\sf a - 10 + b - 10$

$\implies\sf (a + b) - 10 - 10$

$\implies\sf 40 - 20$

$\implies\sf 20$

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the ages of Mother and

Daughter before 10years = 20years

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