A person had two plots of land. In each plot, he cultivated maize and barley. The ratio of the area under maize cultivation to that under barley cultivation in the larger plot is 8 : 9. The ratio of the total areas under maize cultivation and barley cultivation in the two plots together is 29 : 33. The ratio of the areas under maize cultivation and barley cultivation in the smaller plot is 13 : 15. The ratio of the area under maize cultivation in the larger plot to that under barley cultivation in the smaller plot is:

Let us assume that the area under maize and barley in the larger plot is 8x and 9x. 

Similarly, the area under maize and barley in the smaller part is 13y and 15y. 

It is given that the total area under maize and barley (taking both the plots) is in the ratio 29:33.

By this, we get that $$\ \frac{\ 8x+13y}{9x+15y}$$= $$\ \frac{\ 29}{33}$$

This is, 264x+429y=261x+435y, making this as 3x=6y, or x=2y

For the ratio of area under maize (larger plot) to area under barley in smaller plot, we shall substitute the values in 8x:15y

The final ratio is 16y:15y, or 16:15.