Question

9. The sum of the numerator and denominator of a fraction is 8. If 3 is
added to both of the numerator and the denominator, the fraction
3
becomes Find the fraction.
[CBSE 20031
4​

Answer 1

Step-by-step explanation:

Let the numerator be x and denominator be 8-x

x+3/8-x+3=3/4

x+3/11-x=3/4

4(x+3)=3(11-x)

4x +12= 33 -3x

4x+3x=33-12

7x=21

x=3

fraction=x/8-x

3/8-3

ans.3/5

Answer 2

SOLUTION :-

Let,

Numerator = x

Denominator = y

According to the first condition,

$\longrightarrow\sf x +y = 8 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ................(1)$

According to the second condition,

$\longrightarrow\sf \dfrac{x+3}{y+3}=\dfrac{3}{4} \\\\\longrightarrow 4(x+3)= 3(y+3)\\\\\longrightarrow 4x+12 = 3y + 9 \\\\\longrightarrow 4x- 3y = -3 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...............................(2)$

Equation (1) × 3,

$\longrightarrow \sf 3x+3y = 24 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ...................(3)$

Equation (2) + Equation (3),

$\longrightarrow\sf 7x= 21 \\\\\longrightarrow \bf x = 3$

Substitute the value of x in equation (1),

$\longrightarrow \sf 3+y= 8 \\\\\longrightarrow \bf y = 5$

$\bf FRACTION = \dfrac{3}{5}$