Question

The ratio of the present ages of Anupama and her mother is 1 : 7. After 2 years, the ratio become 2:11. Find their present ages.​

Answer 1

Answer:

Present age of Anupama is 6 years.

Present age of her mother is 42 years.

Step-by-step explanation:

Given :

• Ratio of present ages of Anupama and her mother is 1:7 .
• After 2 years, ratio is 2:11.

To find :

• Present ages of Anupama and her mother.

Solution :

Let, Present age of Anupama be 1x or x .

• Ratio of present ages of Anupama and her mother is 1:7.

Therefore, Present age of her mother be 7x .

After 2 years :

Anupama's age = x + 2

Her mother age = 7x + 2

Ratio of their ages after 2 years is 2:11. So,

$\implies \sf \dfrac{x + 2}{7x + 2} = \dfrac{2}{11}$

$\implies \sf 11 \times (x + 2) = 2 \times (7x + 2)$

$\implies \sf 11x + 22 = 14x + 4$

$\implies \sf 11x + 22 - 4 = 14x$

$\implies \sf 11x + 18 = 14x$

$\implies \sf 18 = 14x - 11x$

$\implies \sf 18 = 3x$

$\implies \sf \dfrac{18}{3} = x$

$\implies \pmb{\sf x = 6}$

• Anupama's age = x = 6 years.
• Her mother age = 7x = 7 × 6 = 42 years.

Hence,

Present age of Anupama is 6 years and Present age of her mother is 42 years.

Answer 2

$\begin{gathered}{\pink{\frak{Given }}} \begin{cases} & {\color{blue}{\leadsto}} \: {\sf{Ratio \: of \: present \: ages \: of \: Anupama \: and \: mother \: 1:7 }} \\ \\ & \sf {\color{blue}{\leadsto}} \: {\sf{After \: 2 \: years, \: the \: ratio \: of \: their \: ages \: will \: be \: 2:11 }} \end{cases} \end{gathered}$

$\\ \rule{200pt}{3pt}$

$\begin{gathered}{\pink{\frak{To \: Find }}} \begin{cases} & {\color{blue}{\leadsto}} \: {\sf{ Present \: age \: of \: Anupama \: and \: her \: mother}} \end{cases} \end{gathered}$

$\\ \rule{200pt}{3pt}$

Solution :

$\color{maroon}{❒}$According to the Question :

• Present ages are in the ratio 1:7 .Hence,

$\qquad\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{Anupama}{Mother} = \dfrac{1x}{7x}}}}}}}{\bigstar}$

• After 2 years, their ages will be in the ratio 2:11 .Hence,

$\qquad\large{\bigstar{\underline{\overline{\boxed{\sf{ \dfrac{1x + 2}{7x + 2 } = \dfrac{2}{11}}}}}}}{\bigstar}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

$\color{maroon}{❒}$Let's Cross Multiply :

${\longmapsto{\qquad{\sf{ 11(1x + 2) = 2(7x + 2) }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 11x + 22 = 14x + 4 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 14x - 11x = 22 - 4 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ 3x = 18 }}}} \\ \\ \ {\longmapsto{\qquad{\sf{ x = \cancel\dfrac{18}{3}}}}} \\ \\ \ {\qquad{\textsf{ Value of x = {\pink{\sf{ 6 }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

$\color{maroon}{❒}$Now, The present age :

$\qquad\large{\orange{\underline{\underline{\red{\sf{ Anupama \: = 1x = 1 \times 6 = 6 \: years }}}}}}$

$\\ \qquad\large{\orange{\underline{\underline{\red{\sf{ Mother \: = 7x = 7 \times 6 = 42 \: years }}}}}}$

$\qquad{━━━━━━━━━━━━━━━━━━━━━━}$

$\color{maroon}{❒}$Therefore :

❝ Present age of Anupama is 6 years and the age of her mother is 42 years . ❞

$\\ {\underline{\rule{300pt}{9pt}}}$