This question asks us to calculate a specific ratio based on the data provided in the table about students studying different disciplines across various institutes. We need to find the ratio of the total number of students studying Science in institutes C and D combined to the total number of students studying Computer Science in institutes A and E combined.

Understanding the Data and the Question

The table presents student counts for four disciplines: Arts, Science, Commerce, and Computer Science, across five institutes: A, B, C, D, and E. To answer the question, we need to locate the relevant numbers for the specified institutes and disciplines from the table.

• We need the number of students studying Science in Institute C.
• We need the number of students studying Science in Institute D.
• We need the number of students studying Computer Science in Institute A.
• We need the number of students studying Computer Science in Institute E.

Step-by-Step Calculation of the Ratio

Step 1: Find the number of students studying Science in Institutes C and D

According to the table:

• Number of students studying Science in Institute C = 36
• Number of students studying Science in Institute D = 48

Total number of students studying Science in institutes C and D taken together is the sum of these two numbers.

Total Science students (C + D) $= 36 + 48 = 84$

Step 2: Find the number of students studying Computer Science in Institutes A and E

According to the table:

• Number of students studying Computer Science in Institute A = 57
• Number of students studying Computer Science in Institute E = 55

Total number of students studying Computer Science in institutes A and E taken together is the sum of these two numbers.

Total Computer Science students (A + E) $= 57 + 55 = 112$

Step 3: Calculate the required ratio

The question asks for the ratio of the number of students studying Science in institutes C and D together to the number of students studying Computer Science in institutes A and E together.

Ratio $= \frac{\text{Total Science students (C + D)}}{\text{Total Computer Science students (A + E)}} = \frac{84}{112}$

Step 4: Simplify the ratio

We need to simplify the fraction $\frac{84}{112}$. We can find the greatest common divisor (GCD) of 84 and 112 to simplify the ratio to its lowest terms.

• Factors of 84 are 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84.
• Factors of 112 are 1, 2, 4, 7, 8, 14, 16, 28, 56, 112.

The greatest common divisor (GCD) of 84 and 112 is 28.

Now, divide both the numerator and the denominator by their GCD, 28.

Ratio $= \frac{84 \div 28}{112 \div 28} = \frac{3}{4}$

So, the ratio is $3 : 4$.

Conclusion

The ratio of the number of students studying Science in institutes C and D taken together to the number of students studying Computer Science in institutes A and E taken together is $3 : 4$. This involves reading the data from the table, summing the required numbers, and then simplifying the resulting ratio.

Revision Table: Key Calculations

Ratio = Total Science (C+D) ∶ Total Computer Science (A+E) = 84 ∶ 112

Simplified Ratio = 3 ∶ 4

Additional Information: Data Interpretation Skills

Data interpretation questions, like this one using a table, are common in many exams. They test your ability to read, understand, and analyze data presented in various formats such as tables, charts, and graphs. Key skills for solving data interpretation problems include:

• Carefully reading the question to understand exactly what is being asked.
• Locating the specific data points needed from the table or chart.
• Performing accurate calculations (addition, subtraction, multiplication, division).
• Calculating percentages, averages, or ratios as required.
• Simplifying fractions or ratios correctly.
• Comparing different data points or trends.

Practicing with different types of data representation helps improve speed and accuracy in solving data interpretation questions.