Question 44249
If the numerator of a fraction is increased by 6 and the denominator is decreased by 5, the resulting fraction is 3/4.If the reciprocal of the original fraction is decreased by 1, the resulting fraction is 16/9. Find the original fraction. 
LET ORIGINAL FRACTION =N/D
N.R. S INCREASED BY 6 ...HENCE NEW N.R. =N+6
D.R. IS DECREASED BY 5...NEW D.R. IS ....=D-5
FRACTION IS 
(N+6)/(D-5)=3/4
4(N+6)=3(D-5)
4N+24=3D-15
3D-4N=39..............................I
RECIPROCAL OF ORIGINAL FRACTION =D/N
REDUCED BY 1 ....D/N -1 =(D-N)/N=16/9
9(D-N)=16N
9D-9N=16N
9D-25N=0...............II
EQN.I*3-EQN.II GIVES
9D-12N-9D+25N=117
13N=117
N=117/13=9
3D-4*9=39
3D=39+36=75
D=75/3=25
HENCE ORIGINAL FRACTION IS 9/25