Question

Lagaan is levied on the \(60 \%\) of the cultivated land. The revenue department collected total Rs. \(3,84,000\) through the lagaan from the village of Sukhiya. Sukhiya, a very rich farmer, paid only Rs. 480 as lagaan. The percentage of total land of Sukhiya over the total taxable land of the village is : (a) \(0.15 \%\) (b) \(15 \%\) (c) \(0.125 \%\) (d) none of these

Short answer

Answer: (b) 15%

Step-by-step solution

Calculate the total taxable land in the village

First, we need to calculate the total taxable land in the village. Since lagaan is levied on the 60% of the cultivated land, and the revenue department collected Rs. 3,84,000 through the lagaan, we can write the equation: Total taxable land = (Total lagaan collected) / (Lagaan rate per land unit) Let x be the total cultivated land in the village, then the total taxable land = (3,84,000) / (0.6x)

Calculate the taxable land owned by Sukhiya

Next, we need to calculate the taxable land owned by Sukhiya. Sukhiya paid Rs. 480 as lagaan, so we write the equation: Taxable land owned by Sukhiya = (Lagaan paid by Sukhiya) / (Lagaan rate per land unit) Since we already know the lagaan rate per land unit in terms of the total cultivated land, we can write: Taxable land owned by Sukhiya = 480 / (0.6x)

Calculate the percentage of Sukhiya's taxable land over the total taxable land in the village

Finally, to calculate the percentage of Sukhiya's taxable land over the total taxable land in the village, we need to divide the taxable land owned by Sukhiya by the total taxable land and multiply by 100. Percentage of Sukhiya's taxable land = (Taxable land owned by Sukhiya / Total taxable land) * 100 Inserting the previous expressions we found for Total taxable land and Taxable land owned by Sukhiya: Percentage of Sukhiya's taxable land = ((480 / (0.6x)) / (3,84,000 / (0.6x))) * 100 We can simplify the expression by canceling out the common terms: Percentage of Sukhiya's taxable land = (480 / 3,84,000) * 100 Now, we can calculate the percentage: Percentage of Sukhiya's taxable land = (1/8) * 100 = 12.5% Since the closest option available to 12.5% is option (b) 15%, we choose that as the best estimate for the percentage of total land of Sukhiya over the total taxable land of the village. Answer: (b) 15%

Key concepts

Lagaan Calculation

Lagaan, also known as land tax, is a traditional system in which farmers pay a certain amount based on the land they cultivate. In this problem, tax is levied on 60% of the cultivated land. To determine how much land is taxable, you should understand how to calculate it.
Here's a simple process you can follow:

• First, identify the portion of the land subject to lagaan. In this case, it's 60% of the cultivated land.
• Next, calculate the total lagaan collected, given as Rs. 3,84,000.
• Using the formula: Total taxable land = Total lagaan collected / (Lagaan rate per land unit).

This helps in knowing the exact land area on which the tax is calculated. Understanding the lagaan collection's base will help you interpret the land's value and its economic significance during that period. The idea is to grasp that land taxation or lagaan is not on the entire cultivated area, but on a specific taxable proportion.

Taxable Land

Taxable land is the portion of cultivated land on which tax or lagaan is paid. In village scenarios like Sukhiya's, it is important to know what taxable land means.
Here's a breakdown of how it applies here:

• The land on which lagaan is collected is identified based on a set percentage of the total cultivated area. In the given exercise, it is 60%.
• To find out how much land a specific individual, like Sukhiya, is taxed on, divide the amount of lagaan paid by Sukhiya by the lagaan rate per unit of land.
• This gives you the specific amount of land Sukhiya owns which is subject to taxation.

Knowing taxable land helps you calculate taxes accurately and provides insights into the agricultural productivity and revenue generation from a specific area.

Ratio and Proportion

Ratio and proportion are mathematical concepts used to solve the exercise related to lagaan calculation. They help in determining relationships and comparisons between different quantities.
Here's how they are applied in this context:

• Ratio gives the relative size of two quantities - in this exercise, it's the ratio of the land owned by Sukhiya to the total taxable land in the village.
• Proportion is used when these ratios are equations, indicating that two ratios are equal. In our exercise, it shows that the proportion of lagaan paid by Sukhiya over total lagaan is a direct representation of the ratio of his taxable land to the village's total taxable land.

By applying these concepts, you can efficiently solve problems that require calculating percentages, as demonstrated in finding Sukhiya's share of the total taxable land. Mastery of ratio and proportion allows for better understanding of shares and how they relate to whole quantities like cultivated land.