Question

the denominator of a rational number is greater than its numerator by 3 if numerator is increased by 14 and denominator is decreased by 3 the new number becomes 11 by 4 what is the original number ​

Answer 1

Answer:

Step-by-step explanation:

The required equation is

X+14/X+3-3=11/4

11x=4(X+14)

11x=4x+56

11x-4x=56

7x=56

X=56/7

X=8

Answer 2

HELLO DEAR FRIEND

LET THE FRACTION BE

$\large{ \frac{ \large{x}}{ \large{y}} }$

ATQ,

$\large{x = y - 3} \: ....(1)$

ALSO,

$\large{ \frac{ \large{x + 14}}{ \large{y - 3}} = \large{ \frac{ \large{11}}{ \large{4}} } }$

$\large{4x + 56 = 11y - 33}$

$\large{4x - 11y = - 33 - 56}$

$\large{4x - 11y = - 89}$

BY PUTTING THE VALUE OF X FROM EQUATION (1)

$\large{4(y - 3) - 11y = - 89}$

$\large{4y - 12- 11y = - 89}$

$\large{ - 7y = - 89 + 12}$

$\large{ - 7y = - 77}$

$\large{ y = \frac{ \large{ - 77}}{ \: \: \: \large{ - 7}} }$

$\large \boxed{ y= \boxed{11}}$

PUTTING VALUE OF Y ON EQUATION ..(1)

$\large{x = y - 3} \:$

$\large{x = 11 - 3} \:$

$\large \boxed{ x= \boxed{8}}$

SO, THE FRACTION WILL BE

$\large \boxed{ \frac{ \large{8}}{ \large{11}} }$

HOPE IT HELPS