Understanding the College Admission Data

The question asks for the ratio of students admitted to the Science stream compared to the students admitted to the Engineering stream across all the listed colleges. The provided table contains the number of students admitted to different streams in specific colleges. We need to sum up the total number of students in each of the mentioned streams across all colleges to find the required ratio.

Calculating Total Students in Science Stream

Let's look at the row for the Science stream in the table. We will add the number of students admitted to Science in each college:

• College w: 100 students
• College x: 150 students
• College y: 350 students
• College z: 300 students

Total number of students admitted to the Science stream is the sum:

Total Science students = $100 + 150 + 350 + 300$

Total Science students = $900$

Calculating Total Students in Engineering Stream

Now, let's look at the row for the Engineering stream in the table. We will add the number of students admitted to Engineering in each college:

• College w: 50 students
• College x: 50 students
• College y: 150 students
• College z: 150 students

Total number of students admitted to the Engineering stream is the sum:

Total Engineering students = $50 + 50 + 150 + 150$

Total Engineering students = $400$

Determining the Ratio of Science to Engineering Students

We need to find the ratio of students admitted to the Science stream and the Engineering stream.

Ratio = (Total Science students) : (Total Engineering students)

Ratio = $900 : 400$

To simplify the ratio, we can divide both numbers by their greatest common divisor, which is 100.

Ratio = $\frac{900}{100} : \frac{400}{100}$

Ratio = $9 : 4$

Comparing with Options

Let's compare our calculated ratio with the given options:

• Option 1: $9 : 4$
• Option 2: $7 : 4$
• Option 3: $11 : 5$
• Option 4: $9 : 5$

Our calculated ratio of $9 : 4$ matches Option 1.

Conclusion on Student Admission Ratio

Based on the data from the table, the total number of students admitted to the Science stream is 900, and the total number of students admitted to the Engineering stream is 400. The ratio of students admitted to the Science stream and the Engineering stream is therefore $900 : 400$, which simplifies to $9 : 4$.

Revision Table: Key Calculations for Ratios

Additional Information: Understanding Ratios in Data Analysis

A ratio is a way to compare two or more quantities. In this case, we used a ratio to compare the total number of students in two different streams (Science and Engineering) across multiple colleges. Ratios can be written in several ways, including using a colon (e.g., $9 : 4$), using the word "to" (e.g., 9 to 4), or as a fraction (e.g., $\frac{9}{4}$). Simplifying a ratio means dividing all parts of the ratio by their greatest common divisor until they are in their simplest whole number form. This makes the comparison easier to understand.

Data tables like the one provided are often used to present information clearly. Analyzing data from tables involves identifying the relevant numbers for the question being asked and performing calculations such as summing, averaging, finding differences, or calculating ratios as required. Always double-check which specific data points are needed for the calculation (e.g., admitted students vs. total seats).