Question

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

Answer 1

Given :-

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

Condition :-

• 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 :-

• Find the original fraction

Solution :-

~ Here, we’re given that the ratio of numerator and denominator of a fraction is 3:2. According to the given ratios we can assume the numerator and denominator. Also by the given condition we can form an equation and by solving it we’ll get the original fraction.

_____________

• Let the numerator be ‘3x’  
• Denominator be ‘2x’  

______________

According to the question ::  

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

$\sf \bigg\{ \maltese \;\; Cross\;multiply \bigg\}$  

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

$\sf \implies 12x + 12 = 18x -18$  

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

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

$\sf \implies x = \dfrac{-30}{-6}$  

$\boxed{\sf{ \star \;\; x = 5 }}$

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Hence,  

    $\sf \bullet \;\; Original\;fraction\;is\;\; \dfrac{15}{10}$

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Answer 2

Given :

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

$\: \: \: \:$

To find :

Find the original Fraction.

$\: \: \: \:$

Solution :

$\: \: \: \:$

$\underline{ \boxed{ \bf{Let \: the \: Fraction \: Be = \dfrac{3x}{2x} }}}$

$\: \: \: \:$

We will add 3 to the Numerator and 2 Will be subtracted from the Denominator.

$\: \: \: \:$

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

$\: \: \: \:$

$\: \: \:$$: \sf \implies12x + 12 = 18x - 8$

$\: \: \: \:$

$\: \: \:$$: \sf \implies18x - 12x = 18 + 12$

$\: \: \: \:$

$\: \: \:$$\sf: \implies6x = 30$

$\: \: \: \:$

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

$\: \: \: \:$

Now putting value of x

$\: \: \: \:$

$\: \: \:$$: \implies \sf \dfrac{3x}{2x} = \dfrac{3 \times 5}{2 \times 5}$

$\: \: \: \:$

$\underline{ \boxed{ \red{ \frak {\therefore{The \: orignal \: fraction \: is \dfrac{1}{10}}}}}}$