Question

mother is 30 years old than her daughter. Find daughters age if before 10 years ago ratio of daughter age to mothers age is 1:7​ ( please tell in detail )​

Answer 1

Given : Mother is 30 years older than her daughter .10 years ago, ratio of mother and her daughter was 1:7 .

To Find : Find the age of Daughter

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SolutioN : For Calculating the Ages let us form the Equation first .After solving it we can get the age of Daughter . let's Solve :

$\maltese$ According to the Question :

$\longmapsto$ Let the age of Daughter be y .So,

$\qquad \; \; {\pmb{\sf{ Age \; of \; Daughter = y \; years }}}$

$\longmapsto$ Mother is 30 years older than her Daughter .So,

$\qquad \; \; {\pmb{\sf{ Age \; of \; Mother = 30 + y \; years }}}$

$\longmapsto$ 10 years ago Ratio of their ages is 1:7 .So,

$\qquad \; {\bigstar {\underline{\overline{\boxed{\pmb{\sf{ \bigg\{ \dfrac{y}{30 + y} \bigg\} = \bigg\{ \dfrac{1}{7} \bigg\} }}}}}}} \; \bigstar$

$\maltese$ Let's Cross Multiply :

${\dashrightarrow{\qquad{\sf{ \bigg\{ \dfrac{y}{30 + y} \bigg\} = \bigg\{ \dfrac{1}{7} \bigg\} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \bigg( 7 \times y \bigg) = 1 \bigg( 30 + y \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 7y = 30 + y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 7y - y = 30 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 6y = 30 }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \dfrac{30}{6} }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ y = \cancel\dfrac{30}{6} }}}} \\ \\ \\ \ {\qquad \; \; {\dashrightarrow{\underline{\boxed{\pmb{\frak{ y = 5 }}}}}}} \; {\purple{\bigstar}}$

$\maltese$ Calculating the Present age :

• Daughter = 5 years
• Mother = 30 + y = 30 + 5 = 35 years

$\therefore \;$ Present age of Daughter is 5 years and age of Mother is 35 years .

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