Question

A fraction becomes 1/3 when 1 is subtracted from the numerator and it becomes 1/4 when 8
added to its denominator. Find the original fraction.​

Answer 1

Step-by-step explanation:

let numerator be 'x' and denominator be 'y'

therefore,required fraction = x

y

According to the given condition

x - 1 = 1

y 3

(x-1)×3 = 1×y

3x-3 = y

3x-y =3 ..(1) (transposing 'y' and '3')

According to the second condition

x = 1

y+8 4

x × 4 = (y+8)×1

4x =y+8

4x-y =8 ...(2)(transposing y)

On subtracting equation(1)from(2)

4x -y = 8

- +3x -y = +3

- + -

x = 5

on sustituting th value of 'x' in equation (1)

3x-y =3 ..(1)

3×(5)-y =3

15-y =3

15-3 =y ( transposing y and 3)

12 =y

y = 12

Original fraction= x = 5

y 12

I hope this will surely help you☺

Answer 2

To Find:-

• Find the original fraction.

Given:-

• Fraction becomes 1/3 when 1 is subtracted from the numerator.
• It becomes 1/4 when 8  added to its denominator.

Let the numerator be " x"

And the denominator be " y "

So,

The fraction is x/y

➣ (x - 1)/y = 1/3

➣ 3(x - 1) = y

➣ 3x - 3 = y

➣ 3x = y + 3  ...... ( 1 )

➣ x = (y + 3)/3

And,

8  added to denominator 1/4

➣ x/( y + 8) = 1/4

➣ 4x = y + 8   ...... ( 2 )

➣ 4x - y - 8 = 0

➣ 4 [ (y + 3)/3 ] - y - 8 = 0

➣ (4y + 12 - 3y - 24)/3 = 0

➣ (4y + 12 - 3y - 24) = 0(3)

➣ y - 12 = 0

➣ $\boxed{\bf{\color{yelow}{ \: y \: = \: 12 \: }}}$

Substitute y equation ( 1 ) to get the value of " x ":-

➣ 3x = y + 3  

➣ 3x = 12 + 3

➣ x = 15/3

➣ $\boxed{\bf{\color{yelow}{ \: x \: = \: 5 \: }}}$

So,

The original fraction is 5/12