Let the numerator of the fraction be x. The denominator of a fraction is greater than its numerator by 12.
∴ Denominator of the fraction = (x + 12)
∴ The required fraction = \(\cfrac{x}{x+12}\)
For the new fraction, numerator is decreased by 2.
∴ The new numerator = (x – 2)
Also, denominator is increased by 7.
∴ The new denominator = (x + 12) + 7
= (x + 19)
Since, the new fraction is equivalent to \(\cfrac{1}{2}\)
∴ \(\cfrac{x-2}{x+19} =\cfrac{1}{2}\)
∴ 2(x – 2) = 1(x + 19)
∴ 2x – 4 = x + 19
∴ 2x – x = 19 + 4
∴ x = 23
∴ The required fraction = \(\cfrac{x}{x+12}\)= \(\cfrac{23}{23+12}\) = \(\cfrac{23}{35}\)
∴ The required fraction is \(\cfrac{23}{35}\).
