In two triangles, the ratio of the areas is 4 : 3 and the ratio of their heights is 3 : 4. Find the ratio of their bases.

Let the bases of the two triangles be x and y and their heights be 3h and 4h respectively.
Then,  $\frac{\frac{1}{2}\times x\times 3h}{\frac{1}{2}\times y\times 4h}=\frac{4}{3}\Rightarrow \frac{x}{y}=\frac{4}{3}\times \frac{4}{3}=\frac{16}{9}$ 

Required ratio = 16 : 9.