Question

the numertor of a fraction is 2 less than the denominator if 3 is added to both the numertor ant the denominator the fraction become 3/4 find the fraction
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Answer 1

$\large\bf\pink{Given :-}$

★The numerator of a fraction is 2 less than the denominator.

★If 3 is added to both the numerator and the denominator, the fraction becomes 3/4.

$\large\bf\pink{To\:find :-}$

★Find the fraction

$\large\bf\pink{Solution :-}$

★Let the denominator be x and numerator be (x - 2)

According to the given condition

✒Numerator of a fraction is 2 less than the denominator. If 3 is added to both the numerator and the denominator then fraction becomes 3/4

$\implies \bf \green{ \frac{x - 2+3}{x+3} = \frac{3}{4}}$

$\implies \large\bf \green{ \frac{x + 1}{x + 3} = \frac{3}{4} }$

$\implies \bf \green{4(x + 1) = 3(x + 3)}$

$\implies \bf \green{4x + 4 = 3x + 9}$

$\implies \bf \green{4x - 3x = 9 - 4}$

$\implies \bf \green {∴ x = 5}$

Hence,

${\boxed{\bf \red{Denominator = x = 5}}}$

${\boxed{\bf\red{Numerator = x - 2 = 5 - 2 = 3}}}$

${\large\underline{\boxed{\bf\purple{{Required\:fraction=\bf\dfrac{3}{5}}}}}}$

Answer 2

Question :-

The Numerator of a fraction is 2 less than the Denominator. If 3 is added to both the Numerator ant the Denominator, then the fraction become 3/4. Find the original Fraction.

Solution :-

To Find —

The Original fraction .

Concept —

Let the Denominator be x .

According to the question the Numerator is 2 less than the Denominator .

So, the Numerator will be (x - 2).

Henceforth , the fraction will be $\bf{\dfrac{(x - 2)}{x}}$.

After that it said that 3 is added to both the Numerator and the denominator i.e,

$\bf{\dfrac{(x - 2) + 3}{x + 3}}$.

After adding 3 to it , the fraction becomes ¾ .

Hence, the Equation formed is

$\boxed{\underline{\bf{\dfrac{(x - 2) + 3}{x + 3} = \dfrac{3}{4}}}}$

So by solving this Equation we can find the required value.

Calculation —

Given Equation :-

$:\implies \bf{\dfrac{(x - 2) + 3}{x + 3} = \dfrac{3}{4}}$

By solving it , we get:-

$:\implies \bf{\dfrac{x + 1}{x + 3} = \dfrac{3}{4}}$

By multiplying (x + 3) on both the sides ,we get :-

$:\implies \bf{\dfrac{x + 1}{(x + 3)} \times (x + 3) = \dfrac{3}{4} \times (x + 3)} \\ \\ \\ \\ :\implies \bf{(x + 1) = \dfrac{3x + 9}{4}}$

By multiplying 4 on both the sides ,we get :-

$:\implies \bf{(x + 1) \times 4 = \dfrac{3x + 9}{4} \times 4} \\ \\ \\ \\ :\implies \bf{4x + 4 = \dfrac{3x + 9}{\not{4}} \times \not{4}} \\ \\ \\ \\ :\implies \bf{4x + 4 = 3x + 9} \\ \\ \\ \\ :\implies \bf{4x - 3x = 9 - 4} \\ \\ \\ \\ :\implies \bf{x = 9 - 4} \\ \\ \\ \\ :\implies \bf{x = 5} \\ \\ \\ \\ \therefore \purple{\bf{x = 5}}$

Hence, the denominator is 5 .

Numerator :-

==> (x - 2)

==> 5 - 2

==> 3

Hence, the Numerator is 3.

Thus, the actual fraction is 3/5.