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

Let the numerator and the denominator be x and y respectively

Fraction= x/y

According to the question

Case I

$\frac{x - 1}{y} = \frac{1}{3} \\ 3(x - 1) = y \\ 3x - 3 = y \\ 3x - y = 3 \: \: \: \: \: \: \: \: \: \: \: \: ....(1) \\ Case II \\ \frac{x}{y + 8} = \frac{1}{4} \\ 4x = y + 8 \\ 4x - y = 8 \: \: \: \: \: \: \: \: ......(2)$

Subtract equation (2) from equation( 1), we get

-x= -5

x=5

Substitute the value of x= 5 in equation (1)

3(5)-y=3

15-y=3

-y=3-15

-y= -12

y=12

Therefore,

Fraction=5/12

Answer 2

Answer:

Let the numerator and the denominator be x and y respectively

Fraction= x/y

According to the question

Case I

\begin{gathered} \frac{x - 1}{y} = \frac{1}{3} \\ 3(x - 1) = y \\ 3x - 3 = y \\ 3x - y = 3 \: \: \: \: \: \: \: \: \: \: \: \: ....(1) \\ Case II \\ \frac{x}{y + 8} = \frac{1}{4} \\ 4x = y + 8 \\ 4x - y = 8 \: \: \: \: \: \: \: \: ...2) \\ \end{gathered}

y

x−1

=

3

1

3(x−1)=y

3x−3=y

3x−y=3....(1)

CaseII

y+8

x

=

4

1

4x=y+8

4x−y=8...(2)

Subtract equation (2) from equation( 1), we get

-x= -5

x=5

Substitute the value of x= 5 in equation (1)

3(5)-y=3

15-y=3

-y=3-15

-y= -12

y=12

Therefore,

Fraction=5/12