Question

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12. Numerator and denominator of a fraction are in the ratio of 3 : 5. If 4 is subtracted from the
numerator, it reduces to
. Find the fraction.​

Answer 1

Proper Question :

• The numerator and denominator of a fraction are in ratio 3:5. If 4 is subtracted from the numerator, it reduces to 1\5, what is the fraction?

$\rule{200}1$

Given,

• The Numerator and Denominator of a fraction are in the ratio 3:5.
• If 4 is subtracted from the Numerator then it reduces to 1/5.

To Find,

• The Fraction

Solution :

$\implies$ Suppose the Numerator be x

And, Suppose the Denominator be y

$\mapsto \underline{\sf{\pink{According \ to \ the \ First \ Condition :}}}$

• The Numerator and Denominator of a fraction are in the ratio of 3:5.

$\implies \sf{\dfrac{x}{y} = \dfrac{3}{5}}$

$\implies \boxed{\sf{5x = 3y}}$        1) Equation

$\mapsto \underline{\sf{\pink{According \ to \ the \ Second \ Condition :}}}$

• If 4 is subtracted from the numerator then it reduces to 1/5.

$\implies \sf{\dfrac{x - 4}{y} = \dfrac{1}{5}}$

$\implies \sf{5x - 20 = y}$

$\implies \boxed{\sf{y = 5x - 20}}$      2) Equation

Now Put the Value of y in First Equation :-

$\implies \sf{5x = 3y}$

$\implies \sf{5x = 3(5x - 20)}$

$\implies \sf{5x = 15x - 60}$

$\implies \sf{5x - 15x = - 60}$

$\implies \sf{-10x = -60}$

$\implies \sf{x = \dfrac{60}{10}}$

$\implies \boxed{\sf{x = 6}}$

Now Put the Value of x in Second Equation :-

$\implies \sf{y = 5x - 20}$

$\implies \sf{y = 5(6) - 20}$

$\implies \sf{y = 30 - 20}$

$\implies \boxed{\sf{ y = 10}}$

Therefore,

$\boxed{\bold{\red{The \ Fraction = \dfrac{x}{y} = \dfrac{6}{10}}}}$

$\rule{200}2$

Answer 2

Correct Question:

Numerator and denominator of a fraction are in the ratio of 3 : 5. If 4 is subtracted from the numerator, it reduces to 1/5. Find the fraction.

Answer:

Let the Numerator be 3n and Denominator be 5n of the Fraction.

$\underline{\bigstar\:\textbf{According to the Question :}}$

$:\implies\sf \dfrac{Numerator-4}{Denominator}=\dfrac{1}{5}\\\\\\:\implies\sf\dfrac{3n-4}{5n}=\dfrac{1}{5}\\\\\\:\implies\sf (3n-4)\times5 = 1\times5n\\\\\\:\implies\sf15n-20 = 5n\\\\\\:\implies\sf15n-5n = 20\\\\\\:\implies\sf10n = 20\\\\\\:\implies\sf n=\dfrac{20}{10}\\\\\\:\implies\sf n = 2$

$\rule{150}{1}$

$\bf{\dag}\:\underline{\boxed{\sf Original\:Fraction=\dfrac{3n}{5n}=\dfrac{3(2)}{5(2)}=\dfrac{\textsf{\textbf{6}}}{\textsf{\textbf{10}}}}}$