If 3 is added to the denominator of a rational number then that number becomes $$\frac{1}{3}$$ and if 4 is added to numerator of the same rational number, then it becomes $$\frac{3}{4}$$ then that rational number is

Solution:

Let the rational No. be $$\frac{A}{B}$$

A/Q

$$\frac{A}{B+3}$$ = $$\frac{1}{3}$$  =>3A = B+3   

3A = B+3 => A=$$\frac{1}{3}$$( B+3)   ....(i)

$$\frac{A +4}{B}$$ = $$\frac{3}{4}$$ => 4A +16 = 3B ....(ii)

4A +16 = 3B

$$\frac{4}{3}$$( B+3) + 16 = 3B

$$\frac{4B}{3} $$ + 4 + 16 = 3B

20 = 3B - $$\frac{4B}{3} $$

20 = $$\frac{5B}{3} $$

B=12

Putting in Equation (i)

A = 5

Hence required rational No. is $$\frac{5}{12}$$   Answer