Question

the denominator of a rational number is greater than its numerator by 3 If numerator and denominator are increased by 1 and 4 respectively the number obtained is 1 /2 find the rational number. Answer is 5/8. explain me.​

Answer 1

AnswEr :

Let the Numerator be x, and Denominator be (x + 3) of the rational number.

$\underline{\bigstar\:\textsf{According to the Question Now :}}$

$:\implies\sf \dfrac{Numerator+1}{Denominator+4}=\dfrac{1}{2}\\\\\\:\implies\sf \dfrac{x+1}{(x+3)+4}=\dfrac{1}{2}\\\\\\:\implies\sf\dfrac{x+1}{x+7}=\dfrac{1}{2}\\\\\\:\implies\sf(x + 1)2 = 1(x + 7)\\\\\\:\implies\sf2x + 2 =x + 7\\\\\\:\implies\sf2x - x = 7 - 2\\\\\\:\implies\sf x = 5$

$\rule{120}{2}$

$\therefore\Large\boxed{\sf Rational \: No. = \dfrac{x}{(x+3)}=\red{\dfrac{5}{8}}}$

Answer 2

Answer:

The rational number is 5 / 8

Step-by-step explanation:

We Have :-

Denominator of a rational number is greater than its numerator by 3

Numerator and denominator are increased by 1 and 4 respectively the number obtained is 1 /2

To Find :-

Rational number

Solution :-

Let the numerator be x and denominator be x + 3

$\frac{1+numerator}{4+denominator}= \frac{1}{2} \\\\\frac{x+1}{x+7} = \frac{1}{2} \\\\2x+2=x+7\\\\x= 5\\\\Number = \frac{5}{8}$

The rational number is 5 / 8