Question

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

Answer 1

Given: Numerator and denominator are in the ratio 3:4

◼Let the numerator be 3x  and the denominator be 4x

Increased denominator = 4x+3

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

◼Cross multiplying :

15x=12x+9

15x-12x=9

3x=9  

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

x=3

◼Substituting 'x' value in the ratios, we get

3x=3*3=9

4x=4*3=12  

Therefore the rational number  is $\frac{9}{12}$

By simplifying $\frac{9}{12}$ we get $\frac{3}{4}$

So, the answer is $\frac{3}{4}$