Question

The denominater of a rational number is greater than its numerator by 7. If the

numerator is increased by 17 and denominater is decreased by 6,the new number

becomes 2. Find the original number​

Answer 1

Answer:

17/22

Step-by-step explanation:

Given,

The denominater of a rational number is greater than its numerator by 7.

Let , the numerator of the original fraction be 'x'

$\sf\implies$ Denominater of the original fraction = x + 7.

Original fraction = $\sf\dfrac{x}{x+7}$

If the numerator is increased by 17 and denominater is decreased by 6,the new number becomes 2.

$\implies \: \dfrac{x + 17}{(x + 7) - 6} = \dfrac{2}{1}$

Let's Do :-

$\dfrac{x + 17}{x + 1} = \dfrac{2}{1}$

Doing Cross Multiplication :-

x+17(1) = 2(x + 1)

x + 17 = 2x + 2

17 - 2 = 2x - x

15 = x

$\therefore \: x= 15$

Numerator of original fraction = x = 15

Denominater of original fraction = x + 7 = 15 + 7

= 22

Original fraction = $\sf\dfrac{x}{x+7} = \dfrac{17}{22}$