The question asks about the land reservation requirement under the Tinkathia arrangement in Bihar for indigo cultivation. This system was a significant part of the agricultural practices in certain areas, particularly in Champaran, Bihar.

Understanding the Tinkathia System in Bihar

The Tinkathia system was a land tenure arrangement prevalent in Bihar, especially in the Champaran district during the British rule. Under this system, Indian tenants were forced by European planters to cultivate indigo on a fixed portion of their land. The term "Tinkathia" itself refers to this specific land division requirement.

This arrangement was highly exploitative. The tenants were often forced to sell the indigo they produced at very low, pre-determined prices to the planters, which were not profitable for the farmers. Furthermore, cultivating indigo, a cash crop, on fertile land meant less land was available for food crops, impacting the farmers' food security.

Land Reservation Under Tinkathia System

The core requirement of the Tinkathia system was the mandatory dedication of a specific area of land for indigo cultivation. The arrangement mandated that tenants had to cultivate indigo on three kathas out of every twenty kathas of land they held.

In terms of a fraction, this mandatory reservation can be represented as:

• Three kathas out of twenty kathas
• Fraction = $\frac{3}{20}$

This meant that for every unit of 20 parts of land a farmer owned, 3 parts had to be used for growing indigo, regardless of the farmer's wishes or market conditions. This proportion, $\frac{3}{20}$, is the defining feature of the land reservation under the Tinkathia arrangement.

Analyzing the Options

Let's look at the given options:

• 03/10 ($\frac{3}{10}$)
• 03/20 ($\frac{3}{20}$)
• 03/30 ($\frac{3}{30} = \frac{1}{10}$)
• 03/40 ($\frac{3}{40}$)

Comparing the fraction derived from the description of the Tinkathia system ($\frac{3}{20}$) with the provided options, we find that option 2 matches the correct proportion of land that was required to be reserved for indigo cultivation in Bihar under this system.

The oppressive nature of the Tinkathia system and other similar exploitative practices led to significant unrest among the farmers, eventually culminating in movements like the Champaran Satyagraha led by Mahatma Gandhi.

Therefore, the amount of land that was to be reserved for indigo cultivation under the Tinkathia arrangement was $\frac{3}{20}$ of the total land held by the tenant.