Solving the Game Participation Average Problem

The question asks for the average number of students participating in Carrom from class D and students participating in Chess from class A, based on the provided table data.

First, let's look at the data presented in the table:

The students who participate in either Chess or Carrom are the total students minus those who participate in neither game.

Calculating Students Playing Chess or Carrom

For each class, the number of students who play either Chess or Carrom is given by:

\(\text{Students playing Chess or Carrom} = \text{Total Students} - \text{Students without participation}\)

• Class A: \(420 - 119 = 301\) students
• Class B: \(330 - 88 = 242\) students
• Class C: \(240 - 110 = 130\) students
• Class D: \(125 - 45 = 80\) students
• Class E: \(390 - 130 = 260\) students

These calculated numbers represent the total number of students in each class who play either Chess or Carrom, distributed according to the given ratio.

Calculating Carrom Players from Class D

For Class D:

• Total students playing Chess or Carrom: 80
• Ratio of Chess to Carrom: 2 ∶ 3
• Total parts in the ratio: \(2 + 3 = 5\)

The number of students participating in Carrom from Class D is the fraction of the total players corresponding to the Carrom part of the ratio:

\(\text{Carrom players in D} = \left(\frac{\text{Carrom Ratio Part}}{\text{Total Ratio Parts}}\right) \times \text{Total Players in D}\)

\(\text{Carrom players in D} = \left(\frac{3}{5}\right) \times 80\)

\(\text{Carrom players in D} = 3 \times \left(\frac{80}{5}\right) = 3 \times 16 = 48\)

So, there are 48 students participating in Carrom from Class D.

Calculating Chess Players from Class A

For Class A:

• Total students playing Chess or Carrom: 301
• Ratio of Chess to Carrom: 4 ∶ 3
• Total parts in the ratio: \(4 + 3 = 7\)

The number of students participating in Chess from Class A is the fraction of the total players corresponding to the Chess part of the ratio:

\(\text{Chess players in A} = \left(\frac{\text{Chess Ratio Part}}{\text{Total Ratio Parts}}\right) \times \text{Total Players in A}\)

\(\text{Chess players in A} = \left(\frac{4}{7}\right) \times 301\)

\(\text{Chess players in A} = 4 \times \left(\frac{301}{7}\right) = 4 \times 43 = 172\)

So, there are 172 students participating in Chess from Class A.

Calculating the Average

The question asks for the average of the number of students participating in Carrom from D and Chess from A. The average is calculated as:

\(\text{Average} = \frac{\text{Carrom players in D} + \text{Chess players in A}}{2}\)

\(\text{Average} = \frac{48 + 172}{2}\)

\(\text{Average} = \frac{220}{2}\)

\(\text{Average} = 110\)

The average number of students is 110.

Final Answer Summary

The number of students playing Carrom from Class D is 48. The number of students playing Chess from Class A is 172. The average of these two numbers is 110.

Revision Table: School Game Participation

Here is a summary of the calculations for students playing Chess or Carrom:

We used the calculated values for Carrom in D (48) and Chess in A (172) to find the average.

Additional Information on Data Interpretation

This problem involves data interpretation from a table. Key steps include:

• Understanding the data presented in each column.
• Identifying the relevant data points needed to answer the question.
• Performing calculations based on the data, such as subtraction to find subsets of students.
• Applying ratios to distribute a total number into parts.
• Calculating averages by summing values and dividing by the count of values.
• Paying close attention to which class and which game (Chess or Carrom) are specified in the question.

Data interpretation questions often require breaking down the information and performing multiple steps to reach the final answer. Practicing with different types of tables and charts is helpful.