Question

If 1 is subtracted from the numerator and from the denominator of a fraction, the value obtained is 1/2. If 1 is added to its numerator and to its denominator the resulting value is 2/3. Find the fraction.

Answer 1

Answer:

$\large{ \bold{ \frac{3}{5} }}$

Step-by-step explanation:

let the fraction be

$\frac{x}{y}$

given

$\frac{x - 1}{y - 1} = \frac{1}{2}$

$= > 2x - 2 = y - 1$

$= > 2x - y = 1 \quad\{1\}$

Also.

$\frac{x + 1}{y + 1} = \frac{2}{3}$

$= > 3x + 3 = 2y + 2$

$= > 3x - 2y = - 1 \quad\{2\}$

$\{2\} - 2 \times \{1\}$

$= > (3x - 2y) - (4x - 2y) = - 1 - 2$

$= > x = 3$

$\text{from \: \{1\}}$

$y = 2x - 1$

$= > y = 6 - 1$

$= > y = 5$

Therefore the fraction is

$\frac{3}{5}$

Hope it helps