Question

A fraction will become 9/11 if 2 is added to both numerator and denominator if 3 is subtracted from numerator and added to denominator it becomes 1/4 find the fraction

Answer 1

Answer:

$\large \bold{ \frac{139}{931} }$

Step-by-step explanation:

Let the fraction be

$\frac{x }{y}$

Given

$\frac{x + 2}{y + 2} = \frac{9}{11}$

$= > 11x + 22 = 9y + 18$

$= > 11x - 9y = - 4 \quad \{1\}$

Also.

$\frac{x - 3}{y + 3} = \frac{1}{4}$

$= > 4x - 12 = y + 3$

$= > 4x - y = 15 \quad\{2\}$

$\{1\} - 9 \times \{2\}$

$= > (11x - 9y) - (36x - 9y) = - 4 - 135$

$= > 25x = 139$

$= > x = \frac{139}{25} = 5.56$

$\text{from \: \{2\}}$

$y = 4x + 15$

$= > y = 22.24 + 15$

$= > y = 37.24 = \frac{931}{25}$

Therefore the fraction is

$\frac{ \frac{139}{25} }{ \frac{931}{25} }$

$\frac{139}{931}$

Hope it helps