Question

31. The numerator of a fraction is 6 less than denominator. If 3 is added to the
numerator and 1 is subtracted from the denominator, the fraction is equal to
2/3. Find the original fraction.​

Answer 1

$\underline{\bf{Explanation\::}}$

Let us consider the denominator as x and numerator as (x-6) By using the formula,

Fraction = numerator/denominator =

(x-6)/x (x – 6 + 3)/x = 2/3 (x – 3)/x = 2/3

By cross-multiplying

3(x-3) = 2x 3x – 9 = 2x 3x – 2x = 9 x = 9

∴ The denominator is x = 9,

numerator is (x-6) = (9-6) = 3

And the fraction = numerator/denominator

= (x-6)/x = 3/9

$\textbf{= 1/3}$