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. find the fraction​

Answer 1

Hello friend

Here is your answer

Answer:

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

7

5

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}F=

y

x

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

x+y=12x+y=12

\Rightarrow x=12-y⇒x=12−y .........[1]

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

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

y+3

x

=

2

1

\Rightarrow 2x=y+3⇒2x=y+3 .........[2]

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

2(12-y)=y+32(12−y)=y+3

\Rightarrow 24-2y=y+3⇒24−2y=y+3

\Rightarrow 3y=21⇒3y=21

\Rightarrow y=7⇒y=7

Put back the value of y in [1]

x=12-7x=12−7

\Rightarrow x=5⇒x=5

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

7/5

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Answer 2

Given :-

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

• If the denominator is increased by 3,the fraction become ½.

To find :-

• The fraction = ?

Solution :-

Let the numerator be x

and denominator be y

then,

Fraction will be $\rm\dfrac{x}{y}$

Now,

• x + y = 12 ....................(i)

and,

$\rm\:\dfrac{x}{y+3}=\dfrac{1}{2}$

$\rm\longrightarrow\:x\times{2}=y+3$

$\rm\longrightarrow\:2x=y+3$

$\rm\longrightarrow\:2x-y=3\:................(ii)$

Adding eq(i) and eq(ii),

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

⤇ x + 2x + y - y = 15

⤇ 3x = 15

⤇ x = 15/3

⤇ x = 5

Putting the value of x in equation (i),

x + y = 12

⤇ 5 + y = 12

⤇ y = 12 - 5

⤇ y = 7

Now we have,

• x = 5
• y = 7

Hence,the fraction will be $\rm\dfrac{5}{7}$.