Three years ago, the ratio of ages of Amisha and Namisha was 8:9. Three years from now the ratio will become 11:12. What is the present age of Amisha?

Let the present ages of Amisha and Nimisha be A and N, respectively. 

Three years ago, the ratio of the ages of Amisha and Namisha was 8:9.

$$\dfrac{A-3}{N-3}=\dfrac{8}{9}$$

$$9A-27=8N-24$$

$$9A-8N=3\rightarrow1$$

Three years from now, the ratio will become 11:12.

$$\dfrac{A+3}{N+3}=\dfrac{11}{12}$$

$$12A+36=11N+33$$

$$11N-12A=3\rightarrow2$$

Multiply eq. 1 by 4 and eq. 2 by 3, and then adding them up - 

$$33N-32N=12+9$$

$$N=21$$

Therefore, $$A=19$$

The present age of Amisha is 19 years.