Question

The denominator of a fraction is greater than its numerator by 12. If the numerator is decreased by 2 and the denominator is increased by 7, the new fraction is equivalent to 1/2. find the fraction.

Answer 1

Let the numerator be x

Let the denominator be x + 12

∴ Original fraction = x / x + 12


If numerator decreased by 2 = x - 2 and denominator increased by 7 = x + 12 + 7 = x + 19


According to the given condition,

x - 2 / x + 19 = 1 / 2

Cross multiply

∴ 2(x - 2) = 1(x - 19)

∴ 2x - 4 = x - 19

∴ 2x - x = 19 + 4

∴ x = 23


∴ Numerator ➾ x

➾ $\boxed{\boxed{\textsf{23}}}$


∴ Denominator ➾ x + 12

➾ 23 + 12

➾ $\boxed{\boxed{\textsf{35}}}$



∴ Original fraction = $\boxed{\boxed{\boxed{\dfrac{23}{35}}}}$

Answer 2

$\textbf{SOLUTION :}$



Let the numerator of fraction be x.

The denominator of the fraction is greater than its numerator by 12.

$> \: the \: denominator \: is \: x + 12. \\ \\ > \: the \: fraction \: is \: \frac{x}{x + 12}$

The numerator is decreased by 2.

» the new numerator is x - 2.

The denominator is increased by 7.

» the new denominator is

x + 12 + 7 = x + 19

From the given condition,

$\frac{x - 2}{x + 19} = \frac{1}{2} \\ \\ > \: 2 \: (x - 2) = x + 19 \\ \\ > \: 2x - 4 = x + 19 \\ \\ > \: 2x - x = 19 + 4 \\ \\ > \: x = 23 \: and \: \\ \\ x + 12 = 23 + 12 = 35 \\ \\ > \: \frac{x}{x + 12} \: = \: \frac{23}{35}$

$\textbf{Ans :}$ The fraction is $\frac{23}{35}$