Question

The denominator of a rational no.is greater than its numerator by 3.if 5 is added to the denominator,the no. becomes 1/3.Find the rational number​

1000 Points

Answer 1

Answer:

$\large\boxed{\sf{\dfrac{4}{7}}}$

Step-by-step explanation:

Let the numerator be 'x'

But, denominator is 3 more than it's numerator.

Therefore, we have,

Denominator = (x+3)

Therefore, we will get,

Fraction = x/(x+3)

Now, according to question,

When 5 is added to the denominator, the fraction becomes 1/3

Therefore, we will get,

$= > \dfrac{x}{x + 3 + 5} = \dfrac{1}{3} \\ \\ = > \dfrac{x}{x + 8} = \dfrac{1}{3} \\ \\ = > 3x = x + 8 \\ \\ = > 3x - x = 8 \\ \\ = > 2x = 8 \\ \\ = > x = \dfrac{8}{2} \\ \\ = > x = 4$

Therefore, numerator = 4

Therefore, denominator = (4+3) = 7

Hence, the fraction is 4/7.

Answer 2

Given,

• The denominator of a rational number is 3 greater than its numerator .
• when 5 is added to denominator then the number becomes 1/3 .

To Find,

• The Fraction

Solution,

⇒Suppose the numerator be a

And, Suppose the denominator be b

$\boxed{\bold{\red{ According \ to \ the \ Question \ First \ Condition :}}}$

$\implies \sf{b = a + 3}$......1) Equation

$\boxed{\bold{\purple{According \ to \ the \ Question \ Second \ Condition :}}}$

$\implies \sf{\dfrac{a}{b + 5 } = \dfrac{1}{3}}$

$\implies \sf{3a = b + 5}$

$\implies \sf{3a = a + 5 + 3}$

$\implies \sf{3a - a = 8}$

$\implies \sf{2a = 8}$

$\implies \sf{ a = \dfrac{8}{2}$

$\implies \boxed{\sf{a = 4}}$

Now put the value of a in First Equation :-

$\implies \sf{ b = a + 3}$

$\implies \sf{ b = 4 + 3}$

$\implies \boxed{\sf{ b = 7}}$

Therefore ,

$\boxed{\bold{\red{The \ Fraction = \dfrac{4}{7}}}}$

$\rule{200}2$