Analyzing College Programme Success Data

The question asks us to use the provided table showing the percentage of successful boys and girls in various academic programmes. We need to focus specifically on the B.A. programme and determine the ratio of the total number of boys to the total number of girls, given that the number of successful boys and successful girls in this programme is equal.

Relevant Data from the Table

First, let's look at the data for the B.A. programme from the table:

For the B.A. programme:

• Percentage of successful boys = 80%
• Percentage of successful girls = 60%

Setting up the Relationship

Let's denote the total number of boys in the B.A. programme as \(B_{total}\) and the total number of girls in the B.A. programme as \(G_{total}\).

The number of successfully completing boys in B.A. is 80% of the total boys. Mathematically, this is \(0.80 \times B_{total}\).

The number of successfully completing girls in B.A. is 60% of the total girls. Mathematically, this is \(0.60 \times G_{total}\).

The question states that the number of boys and girls successfully completing the B.A. programme are the same. So, we can set up the following equation:

Calculating the Ratio of Boys to Girls

We are asked to find the ratio of the number of boys to the number of girls, which is \(B_{total} : G_{total}\) or \(\frac{B_{total}}{G_{total}}\).

We can rearrange the equation we set up:

To find the ratio \(\frac{B_{total}}{G_{total}}\), we can divide both sides of the equation by \(G_{total}\) and by 0.80:

Now, we simplify the fraction:

So, the ratio \(\frac{B_{total}}{G_{total}}\) is \(\frac{3}{4}\).

This means the ratio of the number of boys to the number of girls in the B.A. programme is \(3:4\).

Summary of the Ratio Calculation

Given:

• Successful Boys = 80% of Total Boys
• Successful Girls = 60% of Total Girls
• Number of Successful Boys = Number of Successful Girls

Let Total Boys = \(B\), Total Girls = \(G\).

The ratio of boys to girls \(B:G\) is \(3:4\).

Revision Table: Key Concepts for Ratio Problems

Additional Information: Understanding Ratios and Proportions

Ratios are used to show the relative sizes of two or more values. In this problem, the ratio \(3:4\) tells us that for every 3 boys in the B.A. programme, there are 4 girls. It doesn't tell us the exact number of boys or girls, but it gives us their proportion.

When solving problems involving percentages and ratios, it's often helpful to convert percentages to decimals or fractions to make calculations easier, as demonstrated in this solution. Setting up an algebraic equation based on the given conditions is a standard approach to solving such problems.

For instance, if the total number of boys in the B.A. programme was 300, then according to the ratio \(3:4\), the total number of girls would be 400. Let's check the successful students:

• Successful boys = 80% of 300 = \(0.80 \times 300 = 240\)
• Successful girls = 60% of 400 = \(0.60 \times 400 = 240\)

Since the number of successful boys (240) is equal to the number of successful girls (240), this example confirms that a ratio of \(3:4\) for total boys to total girls is consistent with the problem statement.