Question

A fraction is such that the denominator is 5 more than the numerator.if the denominator is increased by 2 The fraction become 1/2 find the original fraction
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Answer 1

the original fraction is 7/12

Answer 2

☯GIVEN :

• The denominator of a fraction is 5 more than its numerator.

• The fraction becomes $\bf{ \dfrac{1}{2}}$, if the denominator is increased by 2.

☯TO FIND :

• Required fraction.

➲SOLUTION :

Let the numerator be x.

Then , denominator = x+5

• After increasing the denominator by 2, the fraction becomes $\bf{ \dfrac{1}{2}}$.

$: \implies\sf{ \dfrac{Numerator}{Denominator + 2 } =\dfrac{1}{2} }$

$: \implies\sf{ \dfrac{x}{(x + 5) + 2 } =\dfrac{1}{2} }$

$: \implies\sf{ \dfrac{x}{x + 5 + 2 } =\dfrac{1}{2} }$

$: \implies\sf{ \dfrac{x}{x + 7} =\dfrac{1}{2} }$

$: \implies\sf{ x \times 2 = x + 7}$

$:\implies\sf{ 2x = x + 7}$

$: \implies\sf{ 2x - x = 7}$

$: \implies{ \underline{ \huge{\boxed{ \purple{\bf{x = 7}}}}}}$

★Numerator :

• $\bf{x = 7}$

★ Denominator :

• Substituting the value of x :

$\longrightarrow {\sf{x+5}}$

$\longrightarrow {\sf{7+5}}$

$\longrightarrow {\bf{12}}$

$\huge {\pink{\therefore}}$ The required fraction is $\bf{\dfrac{7}{12}}$.