Question

Numerator of a fraction is 2 less than the denominator. Ifl is added to the numerator and 3 to the denominator then the fraction becomes 2/3. Find the original fraction. ​

Answer 1

Answer:

Original fraction = $\dfrac{7}{9}$

Explanation:

Given,

Numerator of a fraction is 2 less than the denominator,

If we assume the denominator as $x$

Then,

Numerator will be $(x - 2)$

Now,

1 added to numerator :-

$= (x - 2) + 1$

$= x - 1$

And also,

3 added to the denominator,

$= x + 3$

According to the question,

The fraction becomes ⅔

$\therefore \: \dfrac{(x - 1)}{(x + 3)} = \dfrac{2}{3}$

$\implies \: \dfrac{(x - 1)}{(x + 3)} = \dfrac{2}{3}$

$\implies \: {3(x - 1)} = {2(x + 3)}$

$\implies \: 3x - 3 = 2x + 6$

$\implies \: 3x - 2x = 3 + 6$

$\implies \: x =9$

∴ The denominator is :-

${ \rm \therefore Denominator} = x = \bf 9$

And also, the numerator will be

${ { \rm \therefore Numerator} = x - 2 = 9 - 2 = \bf \: 7}$

Hence, the original fraction is :-

$\rm \: = \dfrac{Numerator}{Denominator} = \dfrac{7}{9}$