Question

The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2. What is the fraction?

Answer 1

Answer:

The required fraction is $F=\frac{5}{7}$

Step-by-step explanation:

Given : The sum of the numerator and denominator of a fraction is 12. If the denominator is increased by 3, the fraction becomes 1/2.

To find : What is the fraction?

Solution : Let the fraction is $F=\frac{x}{y}$

→ The sum of the numerator and denominator of a fraction is 12.

$x+y=12$

$\Rightarrow x=12-y$ .........[1]

→ If the denominator is increased by 3, the fraction becomes 1/2.

$\frac{x}{y+3}=\frac{1}{2}$

$\Rightarrow 2x=y+3$  .........[2]

Put the value of x from [1] in [2]

$2(12-y)=y+3$

$\Rightarrow 24-2y=y+3$

$\Rightarrow 3y=21$

$\Rightarrow y=7$

Put back the value of y in [1]

$x=12-7$

$\Rightarrow x=5$

Therefore, The required fraction is $F=\frac{5}{7}$

Answer 2

Answer:

fraction become 5/7

Step-by-step explanation:

The numerator be x

The denominator be y

fraction become x/y

ATQ

x+y=12 ........ [1] equation

it increased three time in denominator

x/y+3=1/2.

2 x = 2y + 3

2 x -y=3. -......[2 ]equation

from 1 and 2

x+y=12

2 x -y=3.

3x =15

x=5

put in equation 1

5+y=12

y=7

fraction become 5/7