Question

The numerator denominator of a rational no. are in the ratio 3:4.if the denominator is increased by 3 the ratio becomes 3:5find the rational no.​

Answer 1

Given :

⬤ Numerator and Denominator of a Rational Number are in the Ratio 3 : 4.

⬤ If Denominator is increased by 3 the Ratio becomes 3 : 5 .

To Find :

⬤ The Rational Number .

Solution :

Let :

• Numerator be 3x .
• Denominator be 4x .

As given that , If Denominator is Increased by 3 then the Ratio becomes 3:5 . Hence ,

• Denominator = 4x + 3

Now :

According to the Question :-

$\sf{\dfrac{3x}{4x+3}=\dfrac{3}{5}}$

By Cross Multiplication :

5(3x) = 3(4x + 3)

15x = 12x + 9

15x - 12x = 9

3x = 9

x = 9/3

x = 3

Therefore , The Value of x is 3 .

Hence ,

Numerator = 3x

= 3(3)

= 9

Denominator = 4x

= 4(3)

= 12

Therefore , The Numerator is 9 and Denominator is 12 .

Answer 2

Answer :-

Ratio of numberator to denominator is 3 : 4

So, Let the numerator be 3x and denominator be 4x.

According to the question :-

Denominator is increased by 3 :- 4x + 3

So, $\sf New\: fraction = \dfrac{3x}{4x + 3} = \dfrac{3}{5}$

Now, Solving the equation and finding the value of x :-

➩ $\sf \dfrac{3x}{4x + 3} = \dfrac{3}{5}$

➩ $\sf 5(3x) = 3(4x +3)$

➩ $\sf 15x = 12x + 9$

➩ $\sf 15x - 12x = 9$

➩ $\sf 3x = 9$

➩ $\sf x = \dfrac{9}{3}$

➩ $\sf x = 3$

• Numerator = 9
• Denominator = 12

$\boxed{\sf Fraction = \frac{9}{12}}$