Rajesh and Vimal own 20 hectares and 30 hectares of agricultural land, respectively, which are entirely covered by wheat and mustard crops. The cultivation area of wheat and mustard in the land owned by Vimal are in the ratio of 5 : 3. If the total cultivation area of wheat and mustard are in the ratio 11 : 9, then the ratio of cultivation area of wheat and mustard in the land owned by Rajesh is

We are told that Rajesh manages 20 hectares and Vimal manages 30 hectares

For Vimal, we know the distribution of the land between Wheat and Mustard, 5:3
So, wheat area will be, $$\frac{5}{8}\left(30\right)$$
Mustard area will be, $$\frac{3}{8}\left(30\right)$$

Similarly, let us assume that the distribution of crops between Wheat and Mustard to be k:1
Wheat will be, $$\frac{k}{k+1}\left(20\right)$$
Mustard will be, $$\frac{1}{k+1}\left(20\right)$$

We are told that total area of Wheat and Mustard is in the ratio 11:9

Adding them up we get, 
$$\dfrac{\left(\dfrac{150}{8}+\dfrac{20k}{k+1}\right)}{\left(\dfrac{90}{8}+\dfrac{20}{k+1}\right)}=\dfrac{11}{9}$$

$$\dfrac{\left(\dfrac{15}{8}+\dfrac{2k}{k+1}\right)}{\left(\dfrac{9}{8}+\dfrac{2}{k+1}\right)}=\dfrac{11}{9}$$

$$\dfrac{135}{8}+\dfrac{18k}{k+1}=\dfrac{99}{8}+\dfrac{22}{k+1}$$

$$\dfrac{36}{8}=\dfrac{22-18k}{k+1}$$

$$44-36k=9k+9$$

$$45k=35$$

$$k=\dfrac{7}{9}$$

Hence the ratio of distribution of area between Wheat and Mustard for Rajesh is $$\dfrac{7}{9}$$