Calculating Teacher Ratios from University Data

The problem asks us to find the ratio of female teachers in Subject E to male teachers in Subject D, based on the provided table showing the percentage distribution of teachers across subjects and the ratio of male to female teachers within each subject.

We are given that the total number of teachers in the university is 1600.

Step 1: Calculate the Total Number of Teachers in Subject E

According to the table, 14% of the total teachers work in Subject E.

Total teachers in Subject E = 14% of 1600

\(\text{Total teachers in E} = \frac{14}{100} \times 1600\)

\(\text{Total teachers in E} = 14 \times 16\)

\(\text{Total teachers in E} = 224\)

Step 2: Calculate the Number of Female Teachers in Subject E

The ratio of Male to Female teachers in Subject E is given as 9:5.

The total parts in the ratio for Subject E are \(9 + 5 = 14\).

The fraction of female teachers in Subject E is \(\frac{5}{14}\).

Number of female teachers in Subject E = \(\frac{5}{14}\) of Total teachers in Subject E

\(\text{Female teachers in E} = \frac{5}{14} \times 224\)

\(\text{Female teachers in E} = 5 \times \frac{224}{14}\)

\(\text{Female teachers in E} = 5 \times 16\)

\(\text{Female teachers in E} = 80\)

Step 3: Calculate the Total Number of Teachers in Subject D

According to the table, 21% of the total teachers work in Subject D.

Total teachers in Subject D = 21% of 1600

\(\text{Total teachers in D} = \frac{21}{100} \times 1600\)

\(\text{Total teachers in D} = 21 \times 16\)

\(\text{Total teachers in D} = 336\)

Step 4: Calculate the Number of Male Teachers in Subject D

The ratio of Male to Female teachers in Subject D is given as 3:4.

The total parts in the ratio for Subject D are \(3 + 4 = 7\).

The fraction of male teachers in Subject D is \(\frac{3}{7}\).

Number of male teachers in Subject D = \(\frac{3}{7}\) of Total teachers in Subject D

\(\text{Male teachers in D} = \frac{3}{7} \times 336\)

\(\text{Male teachers in D} = 3 \times \frac{336}{7}\)

\(\text{Male teachers in D} = 3 \times 48\)

\(\text{Male teachers in D} = 144\)

Step 5: Calculate the Ratio of Female Teachers in Subject E to Male Teachers in Subject D

We need to find the ratio of (Female teachers in E) : (Male teachers in D).

Ratio = 80 : 144

To simplify the ratio, we find the greatest common divisor (GCD) of 80 and 144. Both numbers are divisible by 8.

\(\frac{80}{8} = 10\)

\(\frac{144}{8} = 18\)

The ratio becomes 10 : 18. Both numbers are divisible by 2.

\(\frac{10}{2} = 5\)

\(\frac{18}{2} = 9\)

The simplified ratio is 5 : 9.

Thus, the ratio of the number of female teachers in Subject E to the number of male teachers in Subject D is 5 : 9.

Summary of Calculations:

Ratio of Female teachers in E to Male teachers in D = 80 : 144 = 5 : 9.

Revision Table: Key Concepts

Additional Information: Data Interpretation Tips

When working with data interpretation problems involving tables and percentages, consider these tips:

• Always identify the total quantity the percentages or ratios are based on. In this case, it's the total of 1600 teachers.
• Read the question carefully to identify exactly which values need to be calculated (e.g., female in E, male in D).
• Break down the calculation into steps: first find the total number for the relevant category (subject), then use the ratio to find the specific sub-category (male/female).
• Be mindful of which part of the ratio corresponds to which group (male or female). The ratio is usually given as Male : Female.
• Simplify ratios at the end to match the options provided.
• Double-check calculations to avoid arithmetic errors.