Question

numerator of a rational number is 5 more than its denominator if 2 is subtracted from numerator and 2 is added to its denominator then number becomes 5 by 4 find the rational numbers​

Answer 1

Solution:

Rational number = Numerator/denominator

Numerator has relation with denominator

☞ Let denominator =x

☞and denominator = x+5

◕Rational number = x+5/x

According to the given condition,

→N-2/D+2 = 5/4

→x+5-2/x+2 = 5/4

→x+3/x+2 = 5/4

→4(x+3) = 5(x+2)

→4x+12=5x+10

→4x-5x=10-12

→-x=-2

→x= 2

☞Rational number = x+5/x

→2+5/2

→7/2

Verification:

→N-2/D+2

→7-2/2+2

→5/4

Hence verified.

Answer 2

Solution :

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

The numerator of a rational number is 5 more than it's denominator if 2 is subtracted from numerator and 2 is added to its denominator then number becomes 5/4.

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

The rational number.

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

Let the numerator be r

Let the denominator be m

$\boxed{\bf{The\:rational\:number=\frac{r}{m} }}}}$

A/q

$\longrightarrow\sf{r=5+m.................(1)}$

&

$\longrightarrow\sf{\dfrac{r-2}{m+2} =\dfrac{5}{4}}\\\\\\\longrightarrow\sf{4(r-2)=5(m+2)\:\:\:[cross-multiplication]}\\\\\\\longrightarrow\sf{4r-8=5m+10}\\\\\\\longrightarrow\sf{4r-5m=10+8}\\\\\\\longrightarrow\sf{4r-5m=18}\\\\\\\longrightarrow\sf{4(5+m)-5m=18\:\:\:[from(1)]}\\\\\\\longrightarrow\sf{20+4m-5m=18}\\\\\\\longrightarrow\sf{20-m=18}\\\\\\\longrightarrow\sf{-m=18-20}\\\\\\\longrightarrow\sf{\cancel{-}m=\cancel{-}2}\\\\\\\longrightarrow\sf{\purple{m=2}}$

Putting the value of m in equation (1),we get;

$\longrightarrow\sf{r=5+2}\\\\\longrightarrow\sf{\purple{r=7}}$

Thus;

$\boxed{\bf{The\:rational\:number=\frac{r}{m}=\frac{7}{2} }}}}$