Understanding the University Teacher Data

The problem provides a table showing the percentage distribution of 1600 teachers across six subjects (A-F) in a university and the ratio of male to female teachers in each subject.

We need to find out what percentage the total number of teachers in Subject-C is of the combined total number of female teachers in Subject-D and Subject-A.

Step 1: Calculate Total Teachers in Each Subject

The total number of teachers in the university is 1600. We can find the number of teachers in each subject using the given percentages.

Step 2: Find the Total Number of Teachers in Subject C

From the table calculation, the total number of teachers in Subject C is:

Total teachers in Subject C $= 12\%$ of $1600 = \frac{12}{100} \times 1600 = 192$

Step 3: Find the Number of Female Teachers in Subject D

The total number of teachers in Subject D is 336. The ratio of Male to Female teachers in Subject D is 3:4.

The total parts in the ratio are $3 + 4 = 7$.

The number of female teachers in Subject D is $\frac{4}{7}$ of the total teachers in Subject D.

Female teachers in Subject D $= \frac{4}{7} \times 336$

Since $336 \div 7 = 48$, we have:

Female teachers in Subject D $= 4 \times 48 = 192$

Step 4: Find the Number of Female Teachers in Subject A

The total number of teachers in Subject A is 208. The ratio of Male to Female teachers in Subject A is 1:7.

The total parts in the ratio are $1 + 7 = 8$.

The number of female teachers in Subject A is $\frac{7}{8}$ of the total teachers in Subject A.

Female teachers in Subject A $= \frac{7}{8} \times 208$

Since $208 \div 8 = 26$, we have:

Female teachers in Subject A $= 7 \times 26 = 182$

Step 5: Calculate Total Female Teachers in Subject D and Subject A Together

Total female teachers in Subject D and Subject A combined = Female teachers in Subject D + Female teachers in Subject A

Total female teachers (D + A) $= 192 + 182 = 374$

Step 6: Calculate the Required Percentage

We need to find what percentage the total number of teachers in Subject C (192) is of the total number of female teachers in Subject D and Subject A together (374).

Required percentage $= \frac{\text{Total teachers in Subject C}}{\text{Total female teachers in Subject D and A}} \times 100\%$

Required percentage $= \frac{192}{374} \times 100\%$

Required percentage $\approx 0.513368 \times 100\%$

Required percentage $\approx 51.34\%$

Rounding to the nearest whole number, the percentage is approximately 51%.

Conclusion

The total number of teachers in Subject C is approximately 51% of the total number of female teachers in Subject D and Subject A together.

Revision Table: Key Calculations

Additional Information on Data Interpretation

Data interpretation questions require careful reading of tables or graphs and performing calculations based on the data presented. It is important to understand the units (percentage, ratio, absolute numbers) and what each value represents.

• Percentages: A percentage represents a part of a whole out of 100. To find the value corresponding to a percentage, multiply the percentage (as a decimal or fraction) by the total value.
• Ratios: A ratio expresses the relationship between two or more quantities. To divide a total quantity according to a ratio, sum the parts of the ratio and divide the total quantity by this sum. Then, multiply the result by each part of the ratio to find the individual quantities. For example, a ratio A:B means for every A units of the first type, there are B units of the second type, making a total of A+B parts.
• Approximation: Some questions ask for approximate values. In such cases, calculations can sometimes be simplified, but it's crucial to perform accurate calculations first and then round, especially when options are close.

Practice with various types of data representation like bar graphs, pie charts, line graphs, and tables is key to mastering data interpretation skills for exams.