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​

Answer 1

Answer:

$\boxed{\purple{\bf Fraction = \dfrac{4}{7}}}$

Step-by-step explanation:

Given that :

• The denominator of a fraction is greater than its numerator by 3.
• If 5 is added to the denominator, the fraction becomes 1/3.

To find :

• The fraction.

Solution:

Let the numerator and denominator be x and y respectively.

★ $\boxed{\bf Original \: fraction = \dfrac{x}{y}}$

According to the question,

The denominator of a fraction is greater than its numerator by 3.

$\sf \implies y = x + 3 \: \: \: \dots (i)$

Again, it is given that ;

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

$\sf \implies \frac{x}{y+5} = \frac{1}{3} \\\\\implies \sf \frac{x}{x + 3 + 5} = \frac{1}{3}$

[ Using equation (i) ]

$\sf \implies \frac{x}{x+8} = \frac{1}{3} \\\\\implies \sf 3x = x + 8\\\\\implies \sf 3x - x = 8 \\\\\implies \sf 2x = 8 \\\\\implies \sf x = \frac{8}{2} \\\\\implies \sf x = 4$

Substituting the value of x in (i),

$\sf \implies y = x + 3 \\\\\implies \sf y = 4 + 3 \\\\\implies \sf y = 7$

Now,

Original fraction = $\sf \dfrac{x}{y}$

                            = $\sf \dfrac{4}{7}$

Hence, the answer is 4/7.

Answer 2

Given :

• 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.

To Find :

• The rational number.

Solution :

Let the numerator of the rational number be x.

Let the denominator of the rational number be y.

Rational number = $\bold{\dfrac{x}{y}}$

Case 1 :

The denominator is greater than the numerator by 3.

Equation :

$\sf{\longrightarrow{y=x+3}}$

$\sf{y-3=x\:\:\:\:\:(1)}$

Case 2 :

If 5 is added to the denominator the rational number becomes 1/3.

Numerator = x

Denominator = ( y + 5)

Equation :

$\sf{\longrightarrow{\dfrac{x}{y+5}=\dfrac{1}{3}}}$

$\sf{\longrightarrow{3x=1(y+5)}}$

$\sf{\longrightarrow{3x=y+5}}$

$\sf{\longrightarrow{3(y-3)=y+5}}$

$\sf{\longrightarrow{3y-9=y+5}}$

$\sf{\longrightarrow{3y-y=5+9}}$

$\sf{\longrightarrow{2y=14}}$

$\sf{\longrightarrow{y=\dfrac{14}{2}}}$

$\sf{\longrightarrow{y=7}}$

Substitute, y = 7 in equation (1),

$\sf{\longrightarrow{y-3=x}}$

$\sf{\longrightarrow{7-3=x}}$

$\sf{\longrightarrow{4=x}}$

$\large{\boxed{\bold{Numerator\:of\:fraction\:=\:x\:=\:4}}}$

$\large{\boxed{\bold{ Denominator \:of\:fraction\:=\:y\:=\:7}}}$

$\large{\boxed{\bold{Fraction\:=\dfrac{x}{y}=\dfrac{4}{7}}}}$