Question

the denominator of a rational number is greater than its numerator by 6.if the numerator is decreased by 1 and denominator is increased by 1 the number obtained is 1/3.find the number​

Answer 1

Let the numerator be x

So,

X + 5 / x + 6 - 3 = 5/4

X + 5 / x + 3 = 5/4

4( x + 5) = 5( x + 3)

4x + 20 = 5x + 15

4x - 5x = 15 - 20

-x = - 5

X = 5

So, the original rational number is :-

5 / (5 + 6)

= 5/11

Answer 2

AnswEr :

5/11

$\bf{\red{\underline{\underline{\bf{Given\::}}}}}$

The denominator of a rational number is greater than it's numerator by 6.If the numerator is decreased by 1 and denominator is increased by 1 the number obtained is 1/3.

$\bf{\red{\underline{\underline{\bf{To\:find\::}}}}}$

The number.

$\bf{\red{\underline{\underline{\bf{Explanation\::}}}}}$

Let the numerator be r

Let the denominator be r+6

A/q

$\leadsto\sf{\underline{\sf{The\:new\:numerator\:=\:\red{r-1}}}}\\\leadsto\sf{\underline{\sf{The\:new\:denominator\:=\:r+6+1=\red{r+7}}}}$

$\mapsto\sf{\dfrac{r-1}{r+7} =\dfrac{1}{3} }\\\\\\\mapsto\sf{3(r-1)=1(r+7)}\\\\\\\mapsto\sf{3r-3=r+7}\\\\\\\mapsto\sf{3r-r=7+3}\\\\\\\mapsto\sf{2r=10}\\\\\\\mapsto\sf{r=\cancel{\dfrac{10}{2} }}\\\\\\\mapsto\sf{\red{r=5}}$

Thus,

$\bf{\small{\boxed{\sf{The\:numerator\:=\:r=\pink{5}}}}}\\\bf{\small{\boxed{\sf{The\:denominator\:=\:r+6=5+6=\pink{11}}}}}$

$\underbrace{\sf{The\:number\:=\:\dfrac{5}{11} }}}}}$