4. Form the pair of linear equations in the following problems and find their solutions (if they exist) by any algebraic method:
(ii) 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.
Let the fraction be x/y
According to the question,
x-1/y = 1/3
⇒ 3x - y = 3... (i)
x/y+8 = 1/4
⇒ 4x - y = 8 ... (ii)
Subtracting equation (i) from equation (ii), we get
x = 5 ... (iii)
Putting this value in equation (i), we get
15 - y = 3
y = 12
Hence, the fraction is 5/12
