Question

in a fraction twice the denominator is 2 less than the numerator if 3 is added to the numerator and to the denominator . the fraction become 4/6 ​

Answer 1

Answer:

Correct question:

In a fraction, twice the numerator is two more than the denominator. If 3 is added to the numerator and to the denominator, then the fraction becomes 2/3.

Solution;

Let the numerator be x and denominator be y.

Then the fraction will be x/y.

Now, it is given that;

Twice the numerator is 2 more than the denominator.

=> 2x = y + 2

=> y = 2x - 2 -------(1)

Also, it is given that;

When 3 is added to the numerator and to the denominator, then the fraction becomes 2/3.

=> (x+3)/(y+3) = 2/3

=> 3(x+3) = 2(y+3)

=> 3x + 9 = 2y + 6

=> 3x + 3 = 2y

Now, putting y = 2x - 2 , we get;

=> 3x + 3 = 2(2x - 2)

=> 3x + 3 = 4x - 4

=> 4x - 3x = 3 + 4

=> x = 7

Now, using eq-(1), we have;

=> y = 2x - 2

=> y = 2•7 - 2

=> y = 14 - 2

=> y = 12.

Thus, the fraction is x/y ie, 7/12

Answer 2

$\huge{\mathfrak{\red{\underline{\underline{Answer:-}}}}}$

Fraction = 7/12

$\large{\mathrm{\blue{\underline{Given:-}}}}$

Let the numerator be a and denominator be b.

So, fraction will be a/b

Twice the numerator is 2 (two) more than numerator.

Hence,

2x = y + 2

y = 2x - 2........(1)

When 3 is added to the numerator and denominator. Then the fraction become 4/6.

So, A. T. Q

$\large{\bf{\frac{(x + 3)}{(y + 3)} =\cancel \frac{4}{6} = \frac{2}{3}}}$

$\large{\mathrm{\blue{\underline{By \: Cross \: multiplication}}}}$

⇒2(y + 3) = 3(x + 3)

⇒2y + 6 = 3x + 9

⇒3x = 2y + 6 - 9

⇒ 3x = 2y - 3........(2)

Put value of y from equation 1 in equation 2

⇒3x = 2(2x - 2) - 3

⇒3x = 4x - 4 - 3

⇒ 3x - 4x = -7

⇒-x = -7

⇒x = 7

$\huge{\boxed{\boxed{x \: = \: 7}}}$

Put value in equation 2

⇒3(7) = 2y - 3

⇒21 = 2y - 3

⇒ 21 + 3 = 2y

⇒ 24 = 2y

⇒12 = y

$\huge{\boxed{\boxed{y \: = \: 12}}}$

So, the fraction become 7/12

$\huge{\rm{\boxed{\boxed{Fraction \: =\: \frac{7}{12}}}}}$