A and B currently have an age ratio of 7 : 3. After 7 years this age ratio will become 2 : 1. After how many years from now will the age ratio between the ages of A and B become 3 : 2?

A and B currently have an age ratio of 7 : 3.

Let's assume the present ages of A and B are 7y and 3y respectively.

After 7 years this age ratio will become 2 : 1.

$$\frac{7y+7}{3y+7}\ =\ \frac{2}{1}$$

7y+7 = 6y+14

7y-6y = 14-7

y = 7

Let's assume that after 'z' years from now will the age ratio between the ages of A and B become 3 : 2.

$$\frac{7y+z}{3y+z}\ =\ \frac{3}{2}$$

Put the value of 'y' in the above equation.

$$\frac{7\times7+z}{3\times7+z}\ =\ \frac{3}{2}$$

$$\frac{49+z}{21+z}\ =\ \frac{3}{2}$$

98+2z = 63+3z

3z-2z = 98-63

z = 35

So after 35 years, we will get the required ratio.