Question

If 3 is added to the denominator of a fraction, it becomes 1/3 and if 4 is added to it's numerator, it
becomes 3/4 The fraction is​

Answer 1

Answer:

The fraction is

$\frac{5}{12}$

Step-by-step explanation:

Let the numerator be x and denominator be y .

Therefore , the fraction is

$\frac{x}{y}$

Now , According to the question ,

$\frac{x}{y + 3} = \frac{1}{3} \\ \implies3x = y + 3 \\ \implies \: y = 3x - 3$

$\frac{x + 4}{y} = \frac{3}{4} \\ \implies4x + 16 = 3y \\ \implies4x + 16 = 3(3x - 3) \\ \implies4x + 16 = 9x - 9 \\ \implies9x - 4x = 16 + 9 \\ \implies5x = 25 \\ \implies \: x = 5$

So

$y = 3 \times 5 - 3 \\ \implies \: y = 15 - 3 \\ \implies \: y = 12$

So the fraction is

$\frac{5}{12}$

Answer 2

Answer:

Let the required fraction be x/y respectively.

According to its question it states that when we add 3 in denominator the fraction becomes 1/3 and if we add 4 in Numerator it becomes 3/4

Therefore, the equation that can be formed is

x/y + 3 = 1/3

3x = y + 3

y = 3x - 3

x + 4/ y = 3/4

4x + 16 = 3y

Substituting y = 3x - 3

4x + 16 = 3(3x - 3)

4x + 16 = 9x - 9

9x - 4x = 16 + 9

5x = 25

x = 25/5

x = 5

Substituting value of x in y = 3x - 3

y = 3(5) - 3

y = 15 - 3

y = 12

Therefore, the required fraction is 5/12