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
$$\frac{A}{B+3}$$ =Â $$\frac{1}{3}$$Â =>3A = B+3Â Â
3A = B+3Â => A=$$\frac{1}{3}$$( B+3)Â Â Â ....(i)
$$\frac{A +4}{B}$$ = $$\frac{3}{4}$$Â => 4A +16 = 3BÂ ....(ii)
4A +16 = 3B
$$\frac{4}{3}$$( B+3) + 16 = 3B
$$\frac{4B}{3} $$ + 4 + 16 = 3B
20 =Â 3B -Â $$\frac{4B}{3} $$
20 = $$\frac{5B}{3} $$
B=12
Putting in Equation (i)
A = 5
Hence required rational No. is $$\frac{5}{12}$$  Answer
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