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 with 1 is to 2 . find the fraction

Answer 1

Denominator =x+12
Numerator=x
Now,
x-2 =numerator
x+19 =Denominator
x-2/x+19=1/2
2x-4=x+19
2x-x=19+4
x=23

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 $\frac{23}{35}$