Three years ago, the ratio of the ages of mother and daughter was 8 : 3. After 4 years ,their ages will be in the ratio 11 : 5. What is present age of mother ( in years ) ?

51

3 years ago                   Mother      :         Daughter

                                       8              :          3

At the present age of mother =  8x + 3  ,  age of daughter = 3x + 3

After 4 years ,

age of Mother = 8x + 7     ,      age of daughter = 3 x + 7

Now ,

\(\frac{8x\; + \; 7}{3x \; +\;  7}\) =\(\frac{11}{5}\)

40x + 35 = 33x + 77

   x = 6

Present age of mother = 8 × 6 + 3 = 51 years