Solving the B.Com. Data Interpretation Problem

This problem requires us to use the data provided in the table for the B.Com. programme and the additional information given to find the total number of girls.

Understanding the Given Data for B.Com. Programme

From the table and the question, we have the following information for the B.Com. programme:

• Percentage of successful Boys in B.Com. = 40%
• Percentage of successful Girls in B.Com. = 60%
• Total number of Boys in B.Com. = 200
• Overall percentage of successful students (Boys + Girls) in B.Com. = 44%

Setting up the Calculation

Let's denote the total number of boys in B.Com. as \(B\) and the total number of girls in B.Com. as \(G\).

We are given that \(B = 200\).

The number of successful boys is 40% of the total number of boys:

\(\text{Successful Boys} = 40\% \text{ of } B = 0.40 \times 200 = 80\)

The number of successful girls is 60% of the total number of girls:

\(\text{Successful Girls} = 60\% \text{ of } G = 0.60 \times G\)

The total number of students in B.Com. is the sum of boys and girls:

\(\text{Total Students} = B + G = 200 + G\)

The total number of successful students in B.Com. is the sum of successful boys and successful girls:

\(\text{Total Successful Students} = \text{Successful Boys} + \text{Successful Girls} = 80 + 0.60G\)

Using the Overall Pass Percentage

We are given that the overall percentage of successful students in B.Com. is 44%. This can be expressed as:

\(\left( \frac{\text{Total Successful Students}}{\text{Total Students}} \right) \times 100 = 44\)

Substitute the expressions we derived:

\(\left( \frac{80 + 0.60G}{200 + G} \right) \times 100 = 44\)

Solving for G

Now, let's solve this equation for \(G\):

Divide both sides by 100:

\(\frac{80 + 0.60G}{200 + G} = \frac{44}{100} = 0.44\)

Multiply both sides by \((200 + G)\):

\(80 + 0.60G = 0.44 \times (200 + G)\)

\(80 + 0.60G = 0.44 \times 200 + 0.44 \times G\)

\(80 + 0.60G = 88 + 0.44G\)

Gather terms with \(G\) on one side and constant terms on the other:

\(0.60G - 0.44G = 88 - 80\)

\(0.16G = 8\)

Divide by 0.16 to find \(G\):

\(G = \frac{8}{0.16}\)

\(G = \frac{8}{\frac{16}{100}} = 8 \times \frac{100}{16} = \frac{800}{16}\)

\(G = 50\)

So, the total number of girls in B.Com. is 50.

Let's quickly verify this:

• Boys = 200, Successful Boys = 40% of 200 = 80
• Girls = 50, Successful Girls = 60% of 50 = 30
• Total Students = 200 + 50 = 250
• Total Successful Students = 80 + 30 = 110
• Overall Success Percentage = \(\left(\frac{110}{250}\right) \times 100 = \left(\frac{11}{25}\right) \times 100 = 11 \times 4 = 44\%\). This matches the given information.

Final Answer

The total number of girls in B.Com. is 50.

Revision Table: B.Com. Data

Additional Information: Percentage Calculations in Data Interpretation

Percentage calculations are fundamental in data interpretation questions, especially those involving proportions or distributions within different categories (like boys and girls in this case). Here are some key points:

• Percentage Definition: A percentage is a fraction of 100. \(X\% = \frac{X}{100}\).
• Calculating a Percentage of a Quantity: To find \(X\%\) of a quantity \(Q\), calculate \(\frac{X}{100} \times Q\).
• Calculating Percentage Change: Percentage change is calculated as \(\left( \frac{\text{New Value} - \text{Old Value}}{\text{Old Value}} \right) \times 100\).
• Calculating Overall Percentage: When combining different groups, the overall percentage is not simply the average of individual percentages unless the groups have equal sizes. It's calculated based on the total count of the relevant item divided by the total count of the whole group, multiplied by 100. As shown in this problem, the overall success rate for B.Com. (44%) is different from the simple average of boy's (40%) and girl's (60%) success rates \(\left( \frac{40+60}{2} = 50\%\right)\) because the number of boys (200) and girls (50) is different.
• Using Variables: When an unknown quantity is involved, represent it with a variable (like \(G\) for the number of girls) and set up an equation based on the given percentages and counts.

Mastering these basic concepts helps in accurately solving data interpretation problems involving percentages.