Question

The numerator of a fraction is 6 less than the denominator. If the numerator is reduced
by 2 and the denominator is increased by 3, the fraction becomes 3/14 fraction. Find the original fraction.​

Answer 1

SOLUTION:-

Let denominator =x

thus numerator =x−6

By condition x

x−6+3= 3+2

3(x−3)=2x

3x−9=2x

x=9

So denominator =x=9

thus numerator ⇒x−6=9−6=3

Original fraction = 9=3

* HOPE THIS HELPS YOU *

Answer 2

solution :-

Let the denominator be x .

Then the numerator is x - 6 .

$∴ \: the \: fraction \: = \frac{x - 6}{x} \\ \\ new \: \: denominator = x + 3 \\ \\ new \: \: numerator = x - 6 - 2 = x - 8 \\ \\ ∴the \: \: new \: fraction \: = \frac{x + 8}{x + 3}$

According to the question,

$\frac{x - 8}{x + 3} = \frac{3}{14 } \\ \\ ⟼ \: \: 14(x - 8) = 3(x + 3) \\ \\ ⟼ \: \: 14x - 112 = 3x + 9 \\ \\ ⟼ \: \: 14x - 3x = 9 + 112 \\ \\ ⟼ \: \: 11x = 121 \\ \\ ⟼ \: \: x = 11 \\ \\ ∴ \: \: the \: \: original \: \: fraction = \frac{x - 6}{x} = \frac{11 - 6}{11} = \frac{5}{11}$