Question

If the numerator of a fraction is increased by 2 and denominator is decreased by 1 becomes 2 by 3 if the numerator is increased by 1 and denominator is increased by 2 is equals 1 by 3 find the fraction

Answer 1

here is your answer
hope it help

Answer 2

Answer:

$\dfrac{2}{7}$

Step-by-step explanation:

Given,

Let the required fraction be $\dfrac{x}{y}$

According to the first condition,

$\dfrac{x\ +\ 2}{y\ -\ 1}\ =\ \dfrac{2}{3}\\\Rightarrow 3x\ +\ 6\ =\ 2y\ -\ 2\\\Rightarrow 3x\ -\ 2y\ =\ -8\Rightarrow 3x\ =\ 2y\ -\ 8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,eqn(1)$

Now according to the second condition,

$\dfrac{x\ +\ 1}{y\ +\ 2}\ =\ \dfrac{1}{3}\\\Rightarrow 3x\ +\ 3\ =\ y\ +\ 2\\\Rightarrow 3x\ =\ y\ -1\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,eqn (2)$

From equation (1) and (2), we get,

$2y\ -\ 8\ =\ y\ -\ 1\\\Rightarrow y\ =\ 7$

From the eqn (1)

$x\ =\ \dfrac{2\times 7\ -\ 8}{3}\\\Rightarrow x\ =\ 2$

Hence the required fraction is $\dfrac{x}{y}\ =\ \dfrac{2}{7}.$