Question

The numerator of a fraction is 2 less than three times of its denominator. If 8 is added to its numerator and 6 is added to its denominator, then new fraction will be 5/3 . Find that fraction ​

Answer 1

Solution :-

Let the denominator of a fraction be x.

Numerator of the fraction = 3x - 2

Given : If 8 is added to its numerator and 6 is added to its denominator, then new fraction will be 5/3.

According to the question,

=> (3x - 2 + 8)/(x + 6) = 5/3

=> 3(3x + 6) = 5(x + 6)

=> 9x + 18 = 5x + 30

=> 9x - 5x = 30 - 18

=> 4x = 12

=> x = 12/4 = 3

Therefore,

Numerator = 3x - 2 = (3 × 3) - 2 = 7

Denominator = x = 3

Hence,

Fraction = 7/3

Answer 2

$\huge \boxed{ \bf{answer}}$

$\boxed{ \bf{solution}}$

Let the numerator be 'y' and

The denominator be 'x'

A/Q,

$\bf{ \: y = 3x - 2} \: \: \:\: - - - - > (1)$

Now,

$\implies \: \: \frac{y + 8}{x + 6} = \frac{5}{3}$

$\implies \: \frac{(3x - 2) + 8}{x + 6} = \frac{5}{3} \: \: \: \ - - - > (from \: 1)$

$\implies \: \frac{3x - 2 + 8}{x + 6} = \frac{5}{3}$

$\implies \: \frac{3x + 6}{x + 6} = \frac{5}{3}$

$\implies \: 3(3x + 6) = 5(x + 6)$

$\implies \: 9x + 18 = 5x + 30$

$\implies \: 4x = 12$

$\implies \: x \: = \: 3$

So,

$\boxed{ \bf{denominator = 3}}$

Now, numerator

=> y = 3x - 2

=> y = 3(3) - 2

=> y = 9 - 2

=> y = 7.

$\boxed{ \bf{numerator = 7}}$

Hence ,

$\boxed{ \bf{fraction \: = \frac{7}{3}}}$