Question

a fraction becomes 1/3 when 2 is subracted from the numerator and it becomes 1/2 when 1 is subtracted from the denominator find the fraction ​

Answer 1

Answer :

• The fraction is 7/15

Given :

• a fraction becomes 1/3 when 2 is subtracted from the numerator
• and it becomes 1/2 when 1 is subtracted from the denominator

To find :

• The fraction

Solution :

Let us assume the fraction as x/y

>> a fraction becomes 1/3 when 2 is subtracted from the numerator.

            $\frac{x-2}{y} =\frac{1}{3} \\\\ 3(x-2)=1 \times y \\\\3x-6=y \\\\ 3x-y=6$

>> it becomes 1/2 when 1 is subtracted from the denominator

              $\frac{x}{y-1} =\frac{1}{2} \\\\ x \times 2 = 1(y-1) \\\\ 2x=y-1 \\\\ 2x-y=-1$

--------------------------

      3x - y = 6 ----- (1)

      2x - y = -1 ----- (2)

After subtracting (2) from (1),

 

      3x - y = 6

      2x - y = -1

(-)  -------------------

           x = 7

     

Substitute in any equation,

     3x - y = 6

     3(7) - y = 6

     21 - y = 6

      y = 21 - 6

       y = 15

---------------------------------------

>>> The fraction is 7/15

 

Answer 2

Answer:

Answer :

The fraction is 7/15

Given :

a fraction becomes 1/3 when 2 is subtracted from the numerator

and it becomes 1/2 when 1 is subtracted from the denominator

To find :

The fraction

Solution :

Let us assume the fraction as x/y

>> a fraction becomes 1/3 when 2 is subtracted from the numerator.

\begin{gathered}\frac{x-2}{y} =\frac{1}{3} \\\\ 3(x-2)=1 \times y \\\\3x-6=y \\\\ 3x-y=6\end{gathered}

y

x−2

=

3

1

3(x−2)=1×y

3x−6=y

3x−y=6

>> it becomes 1/2 when 1 is subtracted from the denominator

\begin{gathered}\frac{x}{y-1} =\frac{1}{2} \\\\ x \times 2 = 1(y-1) \\\\ 2x=y-1 \\\\ 2x-y=-1\end{gathered}

y−1

x

=

2

1

x×2=1(y−1)

2x=y−1

2x−y=−1

--------------------------

3x - y = 6 ----- (1)

2x - y = -1 ----- (2)

After subtracting (2) from (1),

3x - y = 6

2x - y = -1

(-) -------------------

x = 7

Substitute in any equation,

3x - y = 6

3(7) - y = 6

21 - y = 6

y = 21 - 6

y = 15

---------------------------------------

>>> The fraction is 7/15