Question

The age of the mother is 30 years more than her daughter's age.Ten year hence,the mother's age will become three times the daughters age at that time. What is the daughters present age in years? ​

Answer 1

Given :

• The age of the mother is 30 years more than her daughter's age.
• 10 year hence,the mother's age will become three times the daughter's age at that time.

To find :

• Present age of daughter .

Solution :

Consider,

• Present age of mother = x years
• Present age of daughter = y years

According to the 1st condition :-

• The age of mother is 30 years more than her daughter's age .

$\implies\sf{x=y+30...................(1)}$

According to the 2nd condition :-

• 10 year hence,the mother's age will become three times the daughter's age at that time.

After 10 years,

• Age of mother = (x+10) years
• Age of daughter = (y+10) years

$\implies\sf{x+10=3(y+10)}$

$\implies\sf{y+30+10=3y+30\:[Put\:x=(y+30)\: from\:eq(1)]}$

$\implies\sf{y+40=3y+30}$

$\implies\sf{y-3y=30-40}$

$\implies\sf{-2y=-10}$

$\implies\sf{y=5}$

• Present age of daughter = 5 years

Therefore, the present age of daughter is 5 years.

Answer 2

$\huge \mathfrak{Answer:-}$

$\large\underline\mathrm{the \: present \: age \: of \: daughter \: is \: 5 \: year's.}$

$\large\underline\mathrm{Given:-}$

The age of the mother is 30 years more than her daughter's age.

10 year hence,the mother's age will become three times the daughters age at that time.

$\large\underline\mathrm{To \: find}$

present age of mother = x years

present age of daughter = y years

$\large\underline\mathrm{According \: to \: questions.:-}$

The age of mother is 30 years more than her daughter's age.

$\implies$ x = y + 30_____(1)

• 10 year hence,the mother's age will become three times.

$\large\underline\mathrm{After \: 10 \: year's.:-}$

• Age of mother = x + 10 year's
• Age of daughter = y + 10 year's

$\implies$ x + 10 = 3(y + 10)

$\implies$ y + 30 - 10 = 3y + 30 [ put x = y + 30]

$\implies$ y + 40 = 3y + 30

$\implies$ y - 3y = 30 - 40

$\implies$ -2y = -10

$\implies$ y = 5

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{the \: present \: age \: of \: daughter \: is \: 5 \: year's.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$