Question

the denominator of a rational number is greater than its numerator by 8 . if the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2.find the rational number.

Answer 1

Let numerator be d

Since denominator is 8 more than numerator

Then, denominator =x+8

So,rational number =x/x+8

Hence,

numerator is increased by 17

Then new numerator is x+17

Denominator is decreased by 1

Then new denominator is x+8-1=x+7

Then,New rational is x+17/x+7

Since New rational is 3/2

Therefore,

x+17/x+7=3/2

(x+17)×2=3 (x+7)

2x+34=3x+21

34-21=3x-2x

13=x

So rational =x/x+8=13/13+8=13/21

I hope it will help you☺

Answer 2

Let the numerator be x and denominator be x+8.

$\frac{x + 17}{x + 8 - 1} = \frac{3}{2}$

$\frac{x + 17}{x + 7} = \frac{3}{2}$

$2(x + 17) = 3(x + 7)$

$2x + 34 = 3x + 21$

$34 - 21 = 3x - 2x$

$13 = x$

NUMERATOR = 13

DENOMINATOR = 21

$\huge\underline {Fraction = \frac{13}{21} }$