Question

A fraction becomes 3/4 if 3is added to both the
numerates and the denominates. if 1 is subtracted
From the numerater and 1 is added to the denomi-
natas, then it becomes 1/3. Find the fraction.​

Answer 1

Answer:

3/5

Step-by-step explanation:

let the fraction=x/y

f 3 is added to both the  numerates and the denominates.

then x+3/y+3=3/4

4(x+3)=3(y+3)

4x+12=3y+9

4x-3y=-3---------------(1)

=================

if 1 is subtracted  from the numerator and 1 is added to the denominator

then x-1/y+1=1/3

3(x-1)=y+1

3x-y=4

multiply by 3

9x-3y=12-------------(2)

=================

subtract (1) from(2)

5x=12+3=15

x=3

from(2)

9*3-3y=12

-3y=12-27=-15

y=5

so the fraction is:

3/5

Answer 2

Answer:

X=3✔✔ Y=5✔✔

Step-by-step explanation:

$let \: fraction \: be \: \frac{x}{y} \\ according \: to \: question \\ \frac{x + 3}{y + 3} = \frac{3}{4} \\ 4x + 12 = 3y + 9 \\ 4x - 3y = - 3 - - - - - (1) \\ again \\ \frac{x - 1}{y + 1} = \frac{1}{3} \\ 3x - 3 = y + 1 \\ 3x - y = 4 \\ 3x = 4 + y \\ x = \frac{4 + y}{3} - - - - - -( 2) \\ putting \: value \: of \: x \: in \: eqn \: 1 \\ 4 \times \frac{(4 + y)}{3} - \frac{3}{1} = - 3 \\ \frac{16 + 4y - 9y}{3} = - 3 \\ 16 - 5y = - 9 \\ - 5y = - 9 - 16 \\ y = \frac{ - 25}{ - 5} \\ y = 5 \\ putting \: value \: of \: y \: in \: eq \: 1 \\ 4x - 3 \times 5 = - 3 \\ 4x = - 3 + 15 \\ x = \frac{12}{4} \\ x = 3$

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