Question

the sum of numinetor and demominator of a fraction is 8 . if 3 is added in both numinetor and demominator the fraction become 3/4. find the fraction​

Answer 1

Given :

• The sum of numerator and denominator of a fraction is 8 .
• If 3 is added in both numerator and denominator the fraction become 3/4.

To find :

• The fraction.

Solution :

Let the numerator of the fraction be x and the denominator of the fraction be y.

According to 1st condition :-

• The sum of numerator and denominator of a fraction is 8.

$\implies\sf{x+y=8}$

$\implies\sf{x=8-y.........eq(1)}$

According to 2nd condition :-

• If 3 is added in both numerator and denominator the fraction become 3/4.

$\implies\sf{\frac{x+3}{y+3}=\frac{3}{4}}$

$\implies\sf{4x+12=3y+9}$

Put x=8-y from eq(1).

$\implies\sf{4(8-y)+12=3y+9}$

$\implies\sf{32-4y+12=3y+9}$

$\implies\sf{-4y-3y=9-32-12}$

$\implies\sf{-7y=-35}$

$\implies\sf{7y=35}$

$\implies\sf{y=5}$

${\boxed{\bold{y=5}}}$

Now put y = 5 in eq(1) for getting the value of x.

$\implies\sf{x=8-y}$

$\implies\sf{x=8-5}$

$\implies\sf{x=3}$

${\boxed{\bold{x=3}}}$

We know,

${\boxed{\bold{Fraction=\dfrac{Numerator}{Denominator}}}}$

Therefore, the required fraction,

$\sf{Fraction=\dfrac{x}{y}=\dfrac{3}{5}}$

Answer 2

$\huge \mathfrak{Answer:-}$

f = 3/5

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

• The sum of numinetor and demominator of a fraction is 8 .
• if 3 is added in both numinetor and demominator the fraction become 3/4.

$\large\underline\mathrm{To \: find}$

• The fraction.

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

Let numerator of the fraction be x and the denominator of the fraction be y.

The sum of numinetor and demominator of a fraction is 8 .

$\implies$ x + y = 8

$\implies$ x = 8 - y_____(1)

if 3 is added in both numinetor and demominator the fraction become 3/4.

$\implies$ x + 3 / y + 3 = 3/4

$\implies$ 4x + 12 = 3y + 9

$\large\underline\mathrm{put \: x \: = \: 8 \: - \: y \: from \: Eq. \: (1)}$

$\implies$ 4(8 - y) + 12 = 3y + 9

$\implies$ 32 - 4y + 12 = 3y + 9

$\implies$ -4y - 3y = 9 - 32 - 12

$\implies$ -7y = -35

$\implies$ y = 5

$\large\underline\mathrm{Now, }$

$\large\underline\mathrm{put \: y \: = \: 5 \: in \: Eq. \: (1).}$

$\implies$ x = 8 - y

$\implies$ x = 8 - 5

$\implies$ x = 3

$\large\underline\mathrm{fraction \: = \: Numerator \: / \: denominator}$

f = x/y

f = 3/5

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$