Question

the numerator and denominator of a fraction are in the ratio 2:3 if 6 is subtracted from the numerator , the fraction becomes two _ thirds of its original value. find fraction

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Answer 1

Solution :-

Let the numerator and denominator of a fraction be 2x and 3x respectively.

According to the question,

=> (2x - 6)/3x = 2/3 × 2/3

=> (2x - 6)/3x = 4/9

=> 3x × 4 = 9(2x - 6)

=> 12x = 18x - 54

=> 12x - 18x = - 54

=> - 6x = - 54

=> x = - 54/-6 = 9

So,

Numerator = 2x = 2 × 9 = 18

Denominator = 3x = 3 × 9 = 27

Hence,

The fraction = Numerator / Denominator = 18/27

Answer 2

Answer:

The Original Fraction = $\frac{2}{3}$

Step-by-step explanation:

Given,

Ratio of the numerator and denominator = 2 : 3

Let,

Numerator = x

Denominator = y

•°• The Original Fraction = $\frac{x}{y}$

According to the first condition,

$\frac{x}{y}$ = $\frac{2}{3}$

$\implies$ x = $\frac {2y}{3}$ ............ ( 1 )

According to the second condition,

$\frac{x\:-\:6}{y}$ = $\frac{2}{3}$×$\frac{x}{y}$

$\implies$ $\frac{x\:-\:6}{y}$ = $\frac{2x}{3y}$

$\implies$ x - 6 = $\frac{2x}{3}$

$\implies$ x - $\frac{2x}{3}$ = 6

$\implies$ $\frac{x}{3}$ = 6

$\implies$ x = 6 × 3

$\implies$ x = 18

Substituting value of x in eq 1, we get :

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

$\implies$ 18 × 3 = 2y

$\implies$ y = 27

•°• The Original Fraction = $\frac{x}{y}$

= $\frac{18}{27}$

= $\frac{2}{3}$

•°• The Original Fraction = $\frac{2}{3}$