Question

The denominator of a fraction exceeds its numerator by 4. If the numerator and denominator are both increased by 3, the new fraction becomes 4/3. Find the original Fraction

Answer 1

AnswEr:

Let us Consider that the Numerator be x and the Denominator be x + 4.

According to Question,

If the Numerator & Denominator are both increased by 3 fraction becomes $\sf\dfrac{4}{3}.$

So,

$\implies\sf\; \dfrac{x +3}{x + 4 + 3} = \dfrac{4}{3}$

$\implies\sf\; \dfrac{x + 3}{x + 7} = \dfrac{4}{3}$

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$\implies\sf\; 3(x +3) = 4(x +7)$

$\implies\sf\; 3x + 9 = 4x + 28$

$\implies\sf\; 3x - 4x = 28 - 9$

$\implies\sf -x = 19$

$\implies\sf\bold\red{x \:=\: -19}$

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$\implies\sf\; Numerator\: = \;x\: = \: -19$

$\implies\sf\; Denominator\: =\: x\; +\: 4\; =\; -19 \;+ \;4$

$\implies\sf\; -15$

$\implies\sf \dfrac{-19}{-15}$

Hence, The Required Fraction is $\sf\red{\dfrac{19}{15}}.$

Answer 2

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QUESTION :

The denominator of a fraction exceeds its numerator by 4.

The denominator of a fraction exceeds its numerator by 4. If the numerator and denominator are both increased by 3, the new fraction becomes 4/3.

The denominator of a fraction exceeds its numerator by 4. If the numerator and denominator are both increased by 3, the new fraction becomes 4/3. Find the original Fraction.

SOLUTION :

Let the required fraction be X /Y

We have :

Y = X + 4.

Hence the fraction can be written in the following format,

Fraction : X / X + 4,

Now both the numerator and denominator are increased by 3

New Fraction becomes :

New Fraction : X + 3 / X + 7.

This is equal to 4/3.

Hence :

X + 3 / X + 7 = 4 / 3

3 X + 9 = 4 X + 28

X = 19.

Hence the required fraction becomes :

19/ 23.

Answer : Thus the original fraction becomes 19/23.