Understanding the Language Data in the Colony

The problem provides information about the languages spoken by 60 people in a colony. We are given the number of people who speak specific combinations of languages or only certain languages. Our goal is to find the total number of people who speak Hindi based on this data.

Analyzing the Given Information

Let's list the information provided:

• Total number of people in the colony = 60
• Number of people who speak only Bengali = 10
• Number of people who speak only Assamese = 5
• Number of people who speak both Hindi and Odia = 10
• Number of people who speak both Marathi and Hindi = 12
• Number of people who speak English, Tamil, and Marathi = 13
• Number of people who speak both Assamese and Hindi = 5
• The remaining people speak both Bengali and Hindi.

Calculating the Remaining Group

The sum of the people in the explicitly mentioned groups is:

\( \text{Sum} = (\text{Only Bengali}) + (\text{Only Assamese}) + (\text{Hindi and Odia}) + (\text{Marathi and Hindi}) + (\text{English, Tamil and Marathi}) + (\text{Assamese and Hindi}) \)

\( \text{Sum} = 10 + 5 + 10 + 12 + 13 + 5 = 55 \)

These are 55 people accounted for in specific categories.

The remaining people are the total number of people minus the sum of the people in these specific groups:

\( \text{Remaining} = \text{Total People} - \text{Sum} \)

\( \text{Remaining} = 60 - 55 = 5 \)

According to the problem, these 5 remaining people speak both Bengali and Hindi.

Identifying Hindi Speakers

To find the total number of people who speak Hindi, we need to identify all the groups mentioned that include Hindi as a spoken language. These groups are:

• People who speak both Hindi and Odia
• People who speak both Marathi and Hindi
• People who speak both Assamese and Hindi
• People who speak both Bengali and Hindi (the remaining group we calculated)

Note that the groups "only Bengali", "only Assamese", and "English, Tamil and Marathi" do not include Hindi speakers, based on their descriptions.

Calculating the Total Number of Hindi Speakers

Now, we sum the number of people in each of the groups identified as speaking Hindi:

\( \text{Total Hindi Speakers} = (\text{Hindi and Odia}) + (\text{Marathi and Hindi}) + (\text{Assamese and Hindi}) + (\text{Bengali and Hindi}) \)

\( \text{Total Hindi Speakers} = 10 + 12 + 5 + 5 \)

\( \text{Total Hindi Speakers} = 32 \)

Therefore, 32 people in the colony speak Hindi.

Revision Table: Language Data Summary

Sum of Hindi speakers = 10 + 12 + 5 + 5 = 32.

Additional Information: Set Theory and Data Analysis

This type of problem involves analyzing overlapping sets of data, which can often be represented using Venn diagrams. Although a full Venn diagram might be complex with this many languages, breaking down the total population into distinct or overlapping groups based on the given information is a fundamental data analysis technique.

• Set Theory: This problem is a practical application of set theory, dealing with unions and intersections of sets (groups of people speaking certain languages).
• Data Interpretation: Carefully interpreting the language used in the problem statement, such as "only" versus "both" or just listing languages, is crucial to correctly categorizing the people.
• Partitioning Data: The problem implies a way to partition the total group of 60 people into several sub-groups based on language skills.

By systematically accounting for each piece of information and identifying which groups contribute to the total number of Hindi speakers, we arrive at the correct solution.