Question

(1) The numerator and the denominator of a fraction are in the ratio 3 : 2. if
3 is added to the
numerator and 2 is subtracted from the denominator, a new fraction is formed whese value is
Find the original fraction.​

Answer 1

To Find:-

• Find the original fraction.

Given:-

• 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.

Solution:-

Let the fraction be 3x/2x

(3x + 3)/(2x - 2) = 9/4

➭ 4( 3x + 3 ) = 9( 2x - 2 )

➭ 12x + 12 = 18x - 18

➭ 18x - 12x = 18 + 12

➭ 6x = 30

➭ x = 30/6

➭ $\tt { \boxed{ \: x \: = \: 5} }$

So,

The fraction is

➭ 3x / 2x = 15/10

Answer 2

Step-by-step explanation:

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$\text{\Large\underline{\red{Correct\ Question:-}}}$

:$\Longrightarrow$ The numerator and the denominator of a fraction are in the ratio 3 : 2. if

3 is added to thenumerator and 2 is subtracted from the denominator, a new fraction is formed whese value is

Find the original fraction.

$\text{\huge\underline{\orange{To\ find:-}}}$

:$\Longrightarrow$ We have to find the original fraction = ??

$\text{\huge\underline{\blue{Explanation:-}}}$

:$\Longrightarrow$ Ratio of numerator and denominator of the fraction = 3 : 2

:$\Longrightarrow$ Let the numerator be 3x and denominator be 2x.

$\text{\huge\underline{\green{Given:-}}}$

:$\Longrightarrow$ If 3 is added to the numerator and 2 is subtracted from the denominator = $\mathrm{\dfrac{9}{4}}$

:$\Longrightarrow$ $\mathrm{\dfrac{(3x + 3)}{(2x - 2)}\ =\ \dfrac{9}{4}}$

$\text{\large\underline{\purple{According\ to\ the\ question:-}}}$

$\therefore$ $\text{\underline{\underline{\pink{By\ Cross\ Multiplication:-}}}}$

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

:$\Longrightarrow$ 12x + 12 = 18x - 18

:$\Longrightarrow$ 12 + 18 = 18x - 12x

:$\Longrightarrow$ 30 = 6x

:$\Longrightarrow$ $\mathrm{\dfrac{30}{6}\ =\ x}$

:$\Longrightarrow$ 5 = x

:$\Longrightarrow$ $\mathfrak\pink{x\ =\ 5}$

● Numerator of the fraction = 3x = 3(5) = 15.

● Denominator of the fraction = 2x = 2(5) = 10.

■ Fraction = $\mathfrak\pink{\dfrac{3x}{2x}\ =\ \dfrac{15}{10}}$

:$\Longrightarrow$ $\therefore$ Fraction is $\mathfrak\pink{\dfrac{15}{10}}$.

$\text{\huge\underline{\bf{Hence\ Verified}}}$

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