Question

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

Answer 1

`\textsf{The fraction is }: (5)/(12)`

Explanation:

`\textsf{Let the unknown fraction be }(a)/(b)`

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

`\implies (a-1)/(b)=(1)/(3)`

`\implies 3(a-1)=b`

`\implies 3a-3=b`

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

`\implies (a)/(b+8)=(1)/(4)`

`\implies 4a=b+8`

`\implies b=4a-8`

Solve for
`a` by substitution:

`\implies 3a-3=4a-8`

`\implies 3a-4a=-8+3`

`\implies -a=-5`

`\implies a=5`

Substitute found value of
`a` into
`b=4a-8` and solve for
`b`:

`\implies b=4(5)-8`

`\implies b=20-8`

`\implies b=12`

`\textsf{Therefore, the fraction is }: (5)/(12)`