Question

4. The present ages of two girls are in the ratio 2:3. After four years, their ages will be in the ratio 3:4. Find the
age of each girl.​

Answer 1

Given :

• Present ages of two girls are in ratio 2:3.
• After 4 years their ages will be in ratio 3:4.

To Find :

• Present Ages of both girls.

Solution :

$\longmapsto\tt{Let\:the\:age\:of\:girl\:A\:be=2x}$

$\longmapsto\tt{Let\:the\:age\:of\:girl\:B=3x}$

After 4 years :

$\longmapsto\tt{Age\:of\:Girl\:A=2x+4}$

$\longmapsto\tt{Age\:of\:Girl\:B=3x+4}$

A.T.Q :

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

$\longmapsto\tt{4(2x+4)=3(3x+4)}$

$\longmapsto\tt{8x+16=9x+12}$

$\longmapsto\tt{8x-9x=12-16}$

$\longmapsto\tt{-1x=-4}$

$\longmapsto\tt\bold{x=4}$

The value of x is 4..

Therefore :

$\longmapsto\tt{Age\:of\:Girl\:A=2(4)}$

$\longmapsto\tt\bold{8\:yrs}$

$\longmapsto\tt{Age\:of\:Girl\:B=3(4)}$

$\longmapsto\tt\bold{12\:yrs}$

Answer 2

⭐ Given :-

• The present ages of two girls are in the ratio 2:3.

• After four years, their ages will be in the ratio 3:4.

⭐ To Find :-

• The Age Of Each Girl.

⭐ Solution :-

Let the age of,

$\sf{First\:Girl=2x.}$

$\sf{Second\:Girl=3x.}$

After four years, The Age Of,

$\sf{First\:Girl=2x+4.}$

$\sf{Second\:Girl=3x+4.}$

So, According To The Question,

The Equation :-

2x+4/3x+4 = 3/4.

➝ 3(3x+4) = 4(2x+4).

➝ 9x + 12 = 8x + 16.

➝ 9x - 8x = 16 - 12.

➝ x = 4.

So,

• Age Of First Girl = 2x = 8.
• Age Of Second Girl = 3x = 12.