Question

in a fraction twice the numerator is 2 more than the the Dominator if 3 is added to the numerator and the denominator the new fraction is 2 upon 3 find the original number ​

Answer 1

Answer:

$let \: the \: fraction \: be \: \frac{x}{y} \\ as \: per \: condition \\ = > 2x = y + 2 \\ = > 2x - y = 2......................eq.1 \\ \\ = > \frac{x + 3}{y + 3} = \frac{2}{3} \\ = > 3x + 9 = 2y + 6 \\ = > 3x - 2y = - 3.................eq.2 \\ \\ solving \: eq. \: 1 \: and \: 2 \\ 6x - 3y = 6 \\ 6x - 4y = - 6 \\ ...................... \\ = > y = 12 \\ \\ from \: eq.1 \\ x = \frac{12 + 2}{2} = 7 \\ \\ therefore \: the \: original \: fraction \: is \: \frac{7}{12}$