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
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Set the ratio of the second land to the first land as x. Then to get 24/9 in the terms of the first land and second land, we need total corn over total wheat. We can treat the first land's area as 1 and the second land's area as x since the result is a ratio:

\(\frac{\frac{7}{10} + \frac{11}{15}*x}{\frac{3}{10} + \frac{4}{15}*x} = \frac{24}{9} = \frac{8}{3}\)

\(\frac{7}{10} + \frac{11}{15}*x = \frac{4}{5} + \frac{32}{45}x\)

\(\frac{1}{45}x = \frac{4}{5} - \frac{7}{10} = \frac{1}{10}\)

\(x = 9/2\).

Now we know the second land is bigger but we want the ratio of the smaller land to the bigger land, so we reverse it to get 2:9.

Ans: D
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how did you get the second one, \(\frac{7}{10} + \frac{11}{15}*x = \frac{4}{5} + \frac{32}{45}x\)
this eqn ?

Hi sthahvi ,

I had \(\frac{\frac{7}{10} + \frac{11}{15}*x}{\frac{3}{10} + \frac{4}{15}*x} = \frac{8}{3}\) and if I move \(\frac{3}{10} + \frac{4}{15}*x\) to the right side I will obtain the second equation.

\(\frac{4}{5}\) comes from \(\frac{8}{3}\) times \(\frac{3}{10} \) and \(\frac{32}{45}\) comes from \(\frac{8}{3}\) times \(\frac{4}{15}\). Hope this helps!

("@" me next time for a faster reply!)
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For such problems, I find alligations the quickest way.

I took the corn portion i.e 7/10, 11/15 and 24/33. I first got all denominators equal and that makes my fractions as 231/330, 242/330 and 240/330. By finding the distance between 240/330 and 231/330 I get 2 and the distance between 242/330 and 240/330 I get 9. Hence the ratio is 2:9.

Hope this is useful.

The problem seems extremely hard. Is it possible to solve in two minutes?