Question

the denominator of a fraction is 2 more than its numerator.if 5 is added to both then the ratio of the numerator and the denominator of the fraction become 4/5 find the original fraction
please send correct answer step by step I will mark you as brainlest​

Answer 1

Answer:-

The Required Fraction Is $\bf\dfrac{3}{5}.$

Explanation:-

Given:-

• Denominator of a fraction is 2 more than its numerator.

• If 5 is added to both then the ratio of numerator to denominator becomes 4/5 (4:5) i.e. the fraction becomes 4/5.

To Find:-

• The Fraction.

Solution:-

Let the numerator of the fraction be x.

So the denominator will be x+2.

$\\ \bf\mapsto fraction = \frac{x}{x + 2}.$

Also ATQ,

$\\ \bf\mapsto \frac{numerator + 5}{denominator + 5} = \frac{4}{5}.$

$\\ \tt\mapsto \frac{x + 5}{x + 2 + 5} = \frac{4}{5} .$

$\\ \tt\mapsto \frac{x + 5}{x + 7} = \frac{4}{5} .$

$\\ \tt\mapsto5(x + 5) = 4(x + 7).$

$\\ \tt\mapsto5x + 25 = 4x + 28.$

$\\ \tt\mapsto5x - 4x = 28 - 25.$

$\\ \large\mapsto \boxed{ \bf x = 3.}$

$\bf\therefore$ The Fraction Is $\bf\dfrac{x}{x+2}$ = $\bf\dfrac{3}{3+2}$ = $\bf\dfrac{3}{5}.$

Answer 2

Given :-

The  denominator of a fraction is 2 more than its numerator.if 5 is added to both then the ratio of the numerator and the denominator of the fraction become 4/5

To Find :-

Original fraction

Solution :-

Let the number be a

a/a + 2

When 5 added

a + 5/a + 2 + 5 = 4/5

a + 5/a + 7 = 4/5

5(a + 5) = 4(a + 7)

5a + 25 = 4a + 28

5a - 4a = 28 - 25

a = 3

Fraction = a/a + 2 = 3/3 + 2 = 3/5

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