Question: If 4 is subtracted from the numerator of a fraction, its value becomes 1/3. If 5 is added to the denominator of the original fraction its value becomes 1/2. What is the original fraction?

Solution:

Let the numerator of the original fraction be 'x' and the denominator be 'y'. So, the original fraction becomes \frac{x}{y}

According to the question,

Condition I,
If 4 is subtracted  from the numerator of a fraction, its value becomes 1/3.

or, \dfrac{x - 4}{y} = \dfrac{1}{3}

or, 3(x -4) = y

or, y = 3x -12


Condition II,
If 5 is added to the denominator of the original fraction, the value becomes 1/2.

or, \dfrac{x}{y+5} = \dfrac{1}{2}

or, 2x = y +5


Put value of y from equation (i) in equation (ii), we get,

or, 2x = (3x -12) +5

or, 2x = 3x -12 +5

or, 3x -2x -7 = 0

\therefore x = 7

Put value of x in equation (i), we get,

or, y = 3×7 - 12

or, y = 21-12

\therefore y = 9

So, (x,y) = (7,9)

Therefore, the required original fraction is \dfrac{7}{9}.