A farmer has two plots of land of different sizes, and each plot of la

Let the 2 plots be P1 and P2

By the theory of compound mixtures, when V1 Volume/Quantity of a mixture of X and Y which is in the ratio a : b is mixed with V2 Volume/Quantity of another mixture X and Y (i.e the constituents of the 2 mixtures are the same in the ratio p : q, then the final ratio of the constituents is given by

\(\frac{X}{Y}\) = \(\frac{X \space from \space V_1 + X \space from \space V_2 }{Y \space from \space V_1 + Y \space from \space V_2} = \frac{(\frac{a}{a + b})*V_1 + (\frac{p}{p + q})*V_2}{(\frac{b}{a + b})*V_1 + (\frac{q}{p + q})*V_2}\)


\(\frac{24}{9} = \frac{(\frac{11}{11 + 4})*P_1 + (\frac{7}{7 + 3})*P_2}{(\frac{4}{11 + 4})*P_1 + (\frac{3}{7 + 3})*P_2}\)


\(24 * (\frac{4}{15} * P_1 + \frac{3}{10} * P_2) = 9 * (\frac{11}{15} * P_1 + \frac{7}{10} * P_2)\)

\(\frac{72}{10} * P_2 - \frac{63}{10} * P_2 = \frac{99}{15} * P_1 - \frac{96}{15} * P_1 \)


\(\frac{9}{10} * P_2 = \frac{3}{15} * P_1\)

\(\frac{P_2}{P_1} = \frac{3}{15} * \frac{10}{9} = \frac{2}{9}\)


Option D

Arun Kumar