Question

the numeratror and denomiratror of rational number are in ratio 3:4 if denomiratror increased by 3 ratio becomes 3:5 find rational number​

Answer 1

let a ratio be equal to x.

then numerator = 3x

then denominator = 4x

A.T.Q,

3x/4x+3=3/5

15x=12x+9

3x=9

x=3

the no. is 9/12

Answer 2

Ratio of Numerator to Denominator=3:4
Let Ratio=3x:4x

Now Fraction
$\frac{3x}{4x}$
If 3 added to Denominator
4x+3
Fraction Become=3:5

As We know a:b=a/b
Now,
$\frac{3x}{4x + 3} = \frac{3}{5} \\ \\ 3x \times 5 = 3(4x + 3) \\ = 15x = 12x + 9 \\ 15x - 12x = 9 \\ 3x = 9\\ x = \frac{\cancel9}{\cancel3} \\ x = 3$
We know Original Numerator=3x=3×3=9
Original Denominator=4x=4×3=12

$\red{\boxed{\mathbf{Original\: Number=\frac{9}{12}}}}$