Question

The numerator of a rational number is 2 more than 3 times the denominator. If the denominator is increased by 5 and numerator is decreased by 5, the number obtained is
$\frac{3}{5} .$
Find the rational number.​

Answer 1

$\huge \mathcal \colorbox {lightblue}{solution}$

Let the denominator be x , then the numerator = 3x + 2 .

According to the question ,

$\frac{(3x + 2) - 5}{x + 5} = \frac{3}{4}$

$= \frac{3x - 3}{x + 5 } = \frac{3}{4}$

➜ 4(3x-3) = 3(x+5)

➜ 12x - 12 = 3x+15

➜ 12x-3x = 15+12 → 9x = 27

$x = \frac{27}{9} = 3$

Therefore, the numerator, 3x+2 = 3×3+2 = 9+2 = 11 and denominator , x = 3 .

Hence , the required rational number

$\huge \mathcal \blue{ = \frac{11}{3}}$

Answer 2

Step-by-step explanation:

first lets make it in an equation,,

lets assume the denominator as 'x'

so,

the fraction= (3x+2)/x

When both the nos. are changed, then the fraction becomes = {(3x+2)-5}/ x+5

Then when we put it in a fraction,,

=> {(3x+2)-5}/ x+5 = 3/5

Now lets solve for 'x'

-> {(3x+2)-5} = (3/5)*(x+5)

-> {(3x+2)-5} = (3x+15)/5

-> 3x+2-5 = (3x+15)/5

-> (3x+2-5) * 5 = 3x+15

-> 15x + 10 - 25 = 3x + 15

=> 10 - 25 = 3x + 15 - 15x

=-> 10 - 25 - 15 = 3x - 15x

-> 10 - 40 = 3x - 15x

-> -30 = -12x

Therfore => 12x=30

=> 2x = 5

=> x = 2.5 or 5/2

So, the fraction = (3x+15)/x

= (7.5+15)/2.5

= 22.5/2.5

= 225/25

= 9/1