Question

Lagaan is levied on the 60% of the cultivated land. The revenue department collected a total Rs. 384000 through the lagan from the village of Sukhiya. Sukhiya, a very rich farmer, paid only Rs 480 as a lagaan. Find the percentage of total land of Sukhiya over the total taxable land?

Answer 1

Hint: First assume the tax money levied on the 60% cultivated land be x then write the equation for levied tax on Sukhiya’s land and equate it to Rs. 480. Also, write the equation for the tax levied on the total village’s land and equate it to Rs. 384000. From these equations you will get expressions for Sukhiya’s land and the total village’s taxable land then take the percentage of the two.
Complete step-by-step answer:
Let us assume the tax money levied on the 60% cultivated land is x.
Now, we are going to find the tax levied on Sukhiya’s land.
Let us assume the cultivable land of Sukhiya is y then the equation for the tax levied on the Sukhiya’s land is shown below.
$\begin{align}
  & \dfrac{60}{100}y\left( x \right)=480 \\
 & \Rightarrow y=\dfrac{480}{0.6x} \\
\end{align}$
So, the total land of Sukhiya is equal to$\dfrac{480}{0.6x}$.
Now, we are going to find the tax levied on the village's total land.
Let us assume the total cultivable land of the village is z then the equation for the tax levied on the village’s land is shown below.
$\begin{align}
  & \dfrac{60}{100}z\left( x \right)=384000 \\
 & \Rightarrow 0.6z=\dfrac{384000}{x} \\
\end{align}$
So, the total taxable land of the village is equal to$\dfrac{384000}{x}$.
Calculating the percentage of total land of Sukhiya over the total taxable land:
$\dfrac{\text{Total land of Sukhiya}}{\text{Total taxable land of village}}\times 100$
Substituting the value of total land of Sukhiya and village in the above expression of percentage we get,
$\begin{align}
  & \dfrac{\dfrac{480}{0.6x}}{\dfrac{384000}{x}}\times 100 \\
 & =\dfrac{800}{384000}\times 100 \\
 & =0.208 \\
\end{align}$
Hence, the percentage of total land of Sukhiya over the total taxable land is 0.208%.

Note: In the above problem, you might be confused with the language of the problem which is saying that “Find the percentage of total land of Sukhiya over the total taxable land”.
The confusion could be whether the taxable land is Sukhiya’s taxable land or the village’s taxable land.
So, the total taxable land is the village’s total taxable land.
And while solving the problem you might equate total land of the village instead of total taxable land so make sure that in calculating the percentage you have written total village’s taxable land which is 60% of the total village’s cultivated land in the total taxable land.