Question

When the present age of mother is added to the present age of the daughter, the sum is 40 years. what will be their total age after 5 years?

Answer 1

Hey

Than the age is 50 years

Answer 2

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

$\underline{ \mathfrak{ \: \: Given, \: \: }} \\ \\ \text{The sum of present ages of mother } \\ \text{and daughter = 40 years} \\ \\ \underline {\mathfrak{ \: \: To \: \: find : \mapsto}} \\ \\ \text{Sum of the ages of mother and } \\ \text{daughter after 5 years = ?}$

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

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

$\mathfrak{ \: Now, \: } \\ \\ \underline{ \text{ \: After \: 5 \: years \: }} \\ \\ \text{The age of the mother will be (x+5) years} \\ \\ \tt{And,} \\ \\ \text{The age of the daughter will be (y+5) years.} \\ \\ \tt{ \therefore \: \: Sum \: \: of \: \: their \: \: ages \: \: will \: \: be} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{ =(x + 5 ) + (y + 5)} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{ = x + 5 + y + 5} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{= (x + y) + 5 + 5 } \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{= 40 + 10 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [From \: (1)]} \\ \\ \: \: \: \: \: \: \: \: \: \: \tt{= 50 }$

$\therefore \sf{Sum \: \: of \: \: the \: \: ages \: \: of \: \: mother \: \: and } \\ \sf{daughter \: \: after \: \: 5 \: \: years = \red{50 \: \: years}}$