Question

The present age of father and his son are in the ratio 7:3 and the ratio of their ages will be 2:1 after 10 year. then present age of father​

Answer 1

Given : The Present age of father and his son are in the ratio 7:3 .After 10 years, the ratio of their ages will be 1:2 .

To Find : Find the Present age

$\\ \qquad{\rule{200pt}{2pt}}$

SolutioN :

$\dag$ According to the Question :

$\longmapsto$ Present age is in the ratio 7:3 .So :

$\qquad \; \bigstar \; {\underline{\overline{\boxed{\pmb{\sf{ \bigg\{ \dfrac{Father}{Son} \bigg\} = \bigg\{ \dfrac{7y}{3y} \bigg\} }}}}}} \; \bigstar$

$\longmapsto$ After 10 years the ratio of their ages will be 2:1 .So :

$\qquad \; \bigstar \; {\underline{\overline{\boxed{\pmb{\sf{ \bigg\{ \dfrac{7y + 10}{3y + 10} \bigg\} = \bigg\{ \dfrac{2}{1} \bigg\} }}}}}} \; \bigstar$

$\dag$ Cross Multiplying the Equation :

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { \bigg\{ \dfrac{7y + 10}{3y + 10} \bigg\} = \bigg\{ \dfrac{2}{1} \bigg\} } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 2 \bigg( 3y + 10 \bigg) = 1 \bigg( 7y + 10 \bigg) } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 6y + 20 = 7y + 10 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 7y - 6y = 20 - 10 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; \sf { 7y - 6y = 10 } \\ \\ \\ \end{gathered}$

$\begin{gathered} \qquad \; \longrightarrow \; \; {\underline{\boxed{\pmb{\sf{ y = 10 }}}}} \; {\purple{\pmb{\bigstar}}} \\ \\ \\ \end{gathered}$

$\dag$ Calculating the Ages :

• Father = 7y = 7(10) = 70 years
• Son = 3y = 3(10) = 30 years

$\therefore \;$ Age of Father is 70 years and the age of his Son is 30 years .

$\\ \qquad{\rule{200pt}{2pt}}$

Answer 2

Step-by-step explanation:

Let the present ages of father and son be 7x and 3x .

After 10 years, their ages will be 7x+10 and 3 x+10 .

According to the question, we have

$\begin{array}{l} \tt \dfrac{7 x+10}{3 x+10}=\dfrac{2}{1} \\ \\ \tt 1(7 x+10)=2(3 x+10) \\ \\ \tt 7 x+10=6 x+20 \\ \\ \tt 7 x-6 x=20-10 \\ \\ \tt x=10 \end{array}$

Then present age of father is 7x ,

$\text{i.e. 7 \( \times 10=70 \) years.}$