Ravi’s age is $$\frac{3}{5}$$ of Shyam’s age. After x years the ratio of the ages of Ravi and Shyam becomes 5 : 7. If initially the sum of their ages is 32, then what is the value of x ?

Let Present Age of Shyam = s  then

      Present Age of Ravi = $$\ \frac{\ 3}{5}$$s

Given Sum of ages of Ravi and Shyam is 32

$$=$$>     $$\ \frac{\ 3}{5}s+s=32$$

                   $$\ \frac{\ 8}{5}s=32$$

                      $$\ s=20$$               

        Present Age of Shyam = 20

        Present Age of Ravi = $$\ \frac{\ 3}{5}\times\ 20$$

                                           =  12

After 'x' years the ratio of ages of Ravi and Shyam = 5:7

$$=$$>         $$\ \frac{12+x\ }{20+x}=\ \frac{\ 5}{7}$$  

     $$84+7x=100+5x$$

                     $$2x=16$$

                       $$x=8$$