Question

the numerator of a fraction is 3 less than its denominator if we add 1 to both numerator and denominator it becomes equal to find the fraction ​

Answer 1

Answer:

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Answer 2

Appropriate Question :

• The numerator of a fraction is 3 less than the denominator.if 1 is added to both its numerator and denominator,it becomes 2/3. find its fraction

$\rule{200}1$

Given,

• The Numerator of a fraction is 3 less than its denominator .
• If we add 1 to both Numerator and Denominator then its becomes 2/3

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 of a fraction is 3 less than its denominator

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

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

• If We add 1 to both numerator and denominator then its becomes 2/3.

$\implies \sf{\dfrac{x + 1}{y + 1} = \dfrac{2}{3}}$

$\implies \sf{3(x + 1) = 2(y + 1)}$

$\implies \sf{3x + 3 = 2y + 2}$

$\implies \sf{3x - 2y = 2 - 3}$

$\implies \sf{3x - 2y = -1}$

║Now Put the Value of x From the First Equation║

$\implies \sf{3(y - 3) - 2y = -1}$

$\implies \sf{3y - 9 -2y = -1}$

$\implies \boxed{\sf{y = 8}}$

║Now Put the Value of y in First Equation ║

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

$\implies \sf{x = 8 - 3}$

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

Therefore,

$\boxed{\large{\sf{\red{The \ Fraction = \dfrac{x}{y} = \dfrac{5}{8}}}}}$

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