Question

find the fraction which become1/2 when its numerator is increased by 6 and is equal to 1/3 when its denominator is increased by 7

Answer 1

let numerator be X nd denominator be Y
so,
1st case => X+6/Y=1/2
                   X+6 = Y/2
                    Y = 2X +12
2nd case => X/Y+7=1/3
                    X/2X +12+7=1/3                        [putting value of Y from 1st case]
                    X/2X + 19 =1/3
                   3 X=2X +19
                    X=19
now Y = 2X + 12
         = 2(19) + 12
          = 50
hence the fraction is 19/50

hop it helps :):)