Question

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

Answer 1

us assume thenumerator to be =x

Let us assume thedenominator to be =y

Hence the fractionbecomes=x/y

Accordingtothe given condition

(x−1)/y=1/3

⇒y=3x−3 ———-(i)

Accordingtothesecond givencondition,

x/(y+8)=1/4

⇒y+8=4x

⇒y=4x−8 ————(ii)

Combining(i)and(ii) we get,

3x−3=4x−8

⇒3x−4x=−8+3

−x=−5

⇒x=5

from(i)

y=15−3=12

So,the fraction is =5/12

Answer 2

Question:-

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

To Find:-

• Find the fraction.

Solution:-

• Let the numerator be x

• Denominator be y

First ,

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

$\sf\longrightarrow \: \dfrac { x - 1 } { y } = \dfrac { 1 } { 3 }$

$\sf\longrightarrow \: 3( x - 1 ) = y$

$\sf\longrightarrow \: y = 3x - 3 . . . . ( 1 )$

It becomes 1/4 , when 8 is added to its denominator:-

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

$\sf\longrightarrow \: 4x = y + 8 . . . . ( 2 )$

Substitute y in equation ( 2 ):-

$\sf\longrightarrow \: 4x = 3x - 3 + 8$

$\sf\longrightarrow \: 4x - 3x = 8 - 3$

$\sf\longrightarrow \: x = 5$

Now ,

We have to find the value of y:-

$\sf\longrightarrow \: y = 3x - 3$

$\sf\longrightarrow \: y = 3( 5 ) - 3$

$\sf\longrightarrow \: y = 15 - 3$

$\sf\longrightarrow \: y = 12$

Hence ,

• Numerator is 5

• Denominator is 12