Question

The sum of the numerator and denominator of a fraction is 4 more than twice the numerator if the numerator and denominator are increased by 3, they are is the ratio 2 : 3. Determine the fraction..

Answer 1

$\huge{\bf{\underline{\red{Solution :}}}}$

Given,

• The sum of the numerator and denominator is 4 more than twice of numerator .
• Numerator and Denominator both are increased by 3 then the fraction become in the ratio of 2:3

To Find,

• The fraction which after all this condition .

Solution,

⇒ Suppose the numerator be x

And Suppose the denominator be y

According to First Condition :-

$\implies \bold{ x + y = 2x + 4}$

$\implies \bold{y = x + 4}$............1) Equation

According to Second Condition :-

$\implies \bold{\frac{x + 3}{y + 3} = \frac{2}{3}}$

$\implies \bold{3x + 9 = 2y +3}$

$\implies \bold{3x - 2y = -3}$............2) Equation

Now put value of y in In this second Equation :-

$\implies \bold{3x - 2(x + 4) = -3}$

$\implies \bold{3x - 2x - 8 = -3}$

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

Put x value in first equation :-

$\implies \bold{ y = x + 4}$

$\implies \boxed{\bold{ y = 9}}$

Therefore,

The Fraction = $\bold{\boxed{\purple{\dfrac{5}{9}}}}$

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Answer 2

Answer:

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