Question

the denominator of a rational number is greater than its numerator by 5. if the numerator is increased by 11 and denominator deceased by 3 ,the number obtained is 5/2.find the rational number​

Answer 1

Answer:

$\sf The \: required \: rational\: Number \: is\: \dfrac{4}{9}$

SOLUTION

$\sf Let \: us \: Assume \: that \: the \: rational \: number\: is \: \dfrac{x}{y}$

Case :- 1

In the question it is given that the denominator of a rational number is greater than its numerator by 5.

$\implies$

Denominator = Numerator + 5

Here,

Numerator of the rational number  = x

Denominator of the rational number = y

$\implies$

y = x + 5 $\longrightarrow$(1)

Case :- 2

If the numerator is increased by 11 and denominator deceased by 3 ,the number obtained is 5/2.

$\implies$

$\sf \dfrac{x + 11 }{y-3} = \dfrac{5}{2}$

[Now , let us perform Cross-Multiplication.]

$\implies$

2(x+11) = 5(y-3)

$\implies$

2x + 22 = 5y - 15 $\longrightarrow$(2)

SOLVING

Let us Substitute , y = x + 5 as from (1) in (2)

$\implies$

2x + 22 = 5( x + 5 ) - 15

$\implies$

2x + 22 = 5x + 25 - 15

$\implies$

5x - 2x = 22 - 25 + 15

$\implies$

3x = 12

$\implies$

$\sf x = \dfrac{12}{3}$

$\implies$

x = 4.

Now,let us substitute x = 4 in (1).

$\implies$

y = 4 + 5

$\implies$

y = 9.

$\red\bigstar$ Therefore , the Required Rational Number is 4/9.