Question

A fraction becomes 1/3when 1 is subtracted from the numerator and it becomes 1/4 when 8is added to it s denominator. find the fraction

Answer 1

Hey Mate ⭐⭐⭐

Here's ur answer ⤵⤵⤵

Let fraction is x/y

A fraction becomes 1/3 when 1 is subtracted from the numerator

So that

X-1    1

----  = ---

y        3

Cross multiply we get

3x -3  = y                    …(1)

and it becomes 1/ 4 when 8 is added to its denominator

so that

 x      1

___=__

y+8   4

4x = y + 8

Plug the value of y from equation first we get

4x = 3x – 3 + 8

X = 5

Plug this value back in equation first we get

3*5 – 3  = y

15 – 3 = y

12 = y

Fraction => 5/12

Y=12

Hope it helps you! ヅ

✪ Be Brainly ✪

Answer 2

Define x and y:

Let x be the numerator

Let y be the denominator

⇒ Fraction = x/y

Form the first equation:

The fraction becomes 1/3 when 1 is subtracted from the numerator

$\dfrac{x-1}{y} = \dfrac{1}{3}$

Cross-multiply:

y = 3(x - 1)

y = 3x - 3 -----------------[ 1 ]

From the second equation:

The fraction becomes 1/4 when 8 is added to the denominator

$\dfrac{x}{y+8} = \dfrac{1}{4}$

Cross multiply:

4x = y + 8

y = 4x - 8 -----------------[ 2 ]

Put the two equations together:

y = 3x - 3 -----------------[ 1 ]

y = 4x - 8 -----------------[ 2 ]

Equate the 2 equations:

3x - 3 = 4x - 8

Subtract 3x from both sides:

- 3 = x - 8

Add 8 to both sides:

5 = x

x = 5 ----------------- Sub into [ 1 ] to find y

Find y:

y = 3x - 3

y = 3(5) - 3

y = 12

Find the fraction:

x = 5

y = 12

⇒ Fraction = 5/12

Answer: The fraction is 5/12