Question

The numerator and the denominator of a fraction are in the ratio of 3 : 2. If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is
$\frac{9}{4}$
(9÷4). Find the original fraction.

​

Answer 1

$\large \bf \clubs \:  Given :-$

• The numerator and the denominator of a fraction are in the ratio of 3 : 2.

• If 3 is added to the Numerator and 2 is subtracted from the Denominator, it becomes $\dfrac{9}{4}$

-----------------------

$\large \bf \clubs \:  To \: Find :-$

• The Original Fraction.

-----------------------

$\large \bf \clubs \:  Solution :-$

Let Numerator and Denominator of Original Fraction be :

• Numerator = 3x

• Denominator = 2x

So ,

$\sf Original \: Fraction \: is : {\dfrac{\text{ 3x}}{ \text{ 2x}} }$

When 3 is added to the Numerator and 2 is subtracted from the Denominator :

$\sf Fraction \: Becomes : { \dfrac{\text{3x+3}}{\text{2x - 2}} }$

✏ According To Question :

$\dfrac{\text{3x+3}}{\text{2x - 2}} = \frac{9}{4}$

✏ On Cross Multiplying :

$4(\text 3x + 3) = 9(\text 2x - 2)$

$12\text x + 12 = 18\text x - 18$

$18\text x - 12\text x = 18+12$

$6\text x = 30$

$\purple{ \Large :\longmapsto  \underline {\boxed{{\bf x = 5} }}}$

Hence ,

$\large\underline{\pink{\underline{\pmb{\frak{Original\:\:Fraction=\dfrac{15}{10}}}}}}$

Answer 2

Answer:

Given :-

• The numerator and the denominator of a fraction are in the ratio of 3 : 2.
• If 3 is added to the numerator and 2 is subtracted from the denominator, a new fraction is formed whose value is 9/4.

To Find :-

• What is the original fraction.

Solution :-

Let,

$\mapsto \bf{Numerator =\: 3x}$

$\mapsto \bf{Denominator =\: 2x}$

Hence, the original fraction will be :

$\leadsto \sf Original\: Fraction\dfrac{Numerator}{Denominator}$

$\leadsto \sf\bold{\green{Original\: Fraction\dfrac{3x}{2x}}}$

According to the question,

$\implies \bf \dfrac{Numerator + 3}{Denominator - 2} =\: New\: Fraction$

$\implies \sf \dfrac{3x + 3}{2x - 2} =\: \dfrac{9}{4}$

By doing cross multiplication we get,

$\implies \sf 9(2x - 2) =\: 4(3x + 3)$

$\implies \sf 18x - 18 =\: 12x + 12$

$\implies \sf 18x - 12x =\: 12 + 18$

$\implies \sf 6x =\: 30$

$\implies \sf x =\: \dfrac{\cancel{30}}{\cancel{6}}$

$\implies \sf x =\: \dfrac{5}{1}$

$\implies \sf\bold{\purple{x =\: 5}}$

Hence, the required original fraction is :

$\longrightarrow \sf Original\: Fraction =\: \dfrac{3x}{2x}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{3 \times 5}{2 \times 5}$

$\longrightarrow \sf Original\: Fraction =\: \dfrac{\cancel{15}}{\cancel{10}}$

$\longrightarrow \sf\bold{\red{Original\: Fraction =\: \dfrac{3}{2}}}$

${\small{\bold{\underline{\therefore\: The\: original\: fraction\: is\: \dfrac{3}{2}\: .}}}}$