Question

The ratio of the present age of puneet and appu is 2:3.After 3 years the ratio of their age will be 3:4.The present age of puneet will be?

Answer 1

Answer:

The age of Puneeth is 6 years and Appu's age is 9 years.

Step-by-step explanation:

Given :

• Ratio of the ages of Puneet and Appu = 2:3

• After 3 years the ratio = 3:4

To find:

• The present age of Puneet

Solution :

Consider the ratio of present ages as x

Present age = 2x:3x

Consider Puneet's age as 2x

consider Appu's age as 3x

Corresponding fraction of 2x:3x and 3:4  

$\tt{\Rightarrow\dfrac{2x}{3x}\:\:and\:\:\dfrac{3}{4}}$

The equation :

$\tt{\implies\dfrac{2x+3}{3x+3}=\dfrac{3}{4}}$

$\tt{\implies4(2x+3)=3(3x+3)}$

$\tt{\implies8x+12=9x+9}$

$\tt{\implies8x-9x=9-12}$

$\tt{\implies-x=-3}$

$\tt{\implies x=3}$

${\boxed{\sf \: {x=3}}}$

Value of 2x =

$\tt{\implies2\times3}$

$\tt{\implies6}$

${\boxed{\sf \: {Puneet's\:age =6}}}$

Value of 3x =

$\tt{\implies3\times3}$

$\tt{\implies9}$

${\boxed{\sf \: {Appu's\:age =9}}}$

∴ The age of Puneeth is 6 years and Appu's age is 9 years.

Verification :-

$\tt{\implies\dfrac{(2\times3)+3}{(3\times3)+3}=\dfrac{3}{4}}$

$\tt{\implies{\dfrac{9}{12}=\dfrac{3}{4}}}$

Divide 9 and 12 by 3

$\tt{\implies{\dfrac{3}{4}=\dfrac{3}{4}}}$

Here, when we placed the vakue of x we got the required answer.

${\boxed{\sf{LHS=RHS}}}$

∴ The age of Puneeth is 6 years and Appu's age is 9 years.

Answer 2

$\mathfrak{Answer:}$

= Puneet's age = 6 years   &    Appu's age = 9 years.

$\mathfrak{Step-by-Step\;Explanation:}$

Let the age of Puneet and Appu be 2x years and 3x years respectively.

After 3 years,

• Puneet's age will be = ( 2x + 3 ) years.
• Appu's age will be = ( 3x + 3 ) years.

$\mathfrak{According\:to\:Question:}$

$\implies\tt{\dfrac{2x+3}{3x+3}=\dfrac{3}{4}}\\\\\\\implies\tt{(2x+3)4=(3x+3)3}\\\\\\\implies\tt{8x+12=9x+9}\\\\\\\implies\tt{9x-8x=12-9}\\\\\\\therefore\quad\tt{x=3.}\\\\\\\\\textbf{Present age of Puneet = 2x years.}\\\\\\\tt{=2\times 3}\\\\\\\tt{=6\;years.}$

$\textbf{Present age of Appu = 3x years.}\\\\\\\tt{=3\times 3}\\\\\\\tt{=9\;years.}\\\\\\\\\boxed{\boxed{\bold{Puneet's\;age=6\;years\quad\&\quad Appu's\;age=9\;years.}}}$