Let's break down this data interpretation question step by step to find the ratio of males in Organisation A to males in Organisation C. We are given the total number of employees across five organisations (A to E), the percentage of employees in each organisation, and the ratio of male to female employees within each organisation.

The total number of employees across all five organisations is 35,000.

Calculating Employees in Organisation A and C

First, we need to find the total number of employees working in Organisation A and Organisation C using the given percentages and the total number of employees.

• Organisation A: The percentage of employees in Organisation A is 18%.
• Total employees in Organisation A = $\text{Total employees} \times \frac{\text{Percentage in A}}{100}$
• Total employees in Organisation A = $35000 \times \frac{18}{100} = 350 \times 18 = 6300$

• Organisation C: The percentage of employees in Organisation C is 31%.
• Total employees in Organisation C = $\text{Total employees} \times \frac{\text{Percentage in C}}{100}$
• Total employees in Organisation C = $35000 \times \frac{31}{100} = 350 \times 31 = 10850$

Calculating Number of Males in Organisation A and C

Next, we use the male to female ratio for each organisation to find the number of male employees. The ratio is given as Male : Female.

For a ratio $M : F$, the proportion of males is $\frac{M}{M+F}$.

• Organisation A: The male to female ratio is 3 : 7.
• Sum of ratio parts = $3 + 7 = 10$
• Proportion of males in A = $\frac{3}{10}$
• Number of males in Organisation A = $\text{Total employees in A} \times \text{Proportion of males in A}$
• Number of males in Organisation A = $6300 \times \frac{3}{10} = 630 \times 3 = 1890$

• Organisation C: The male to female ratio is 3 : 2.
• Sum of ratio parts = $3 + 2 = 5$
• Proportion of males in C = $\frac{3}{5}$
• Number of males in Organisation C = $\text{Total employees in C} \times \text{Proportion of males in C}$
• Number of males in Organisation C = $10850 \times \frac{3}{5} = 2170 \times 3 = 6510$

Finding the Ratio of Males in A to Males in C

Finally, we need to find the ratio of the number of males in Organisation A to the number of males in Organisation C.

• Ratio = Number of males in A : Number of males in C
• Ratio = 1890 : 6510

To simplify the ratio, we can divide both numbers by their greatest common divisor. First, let's divide by 10:

• Ratio = 189 : 651

Now, let's find common factors for 189 and 651. Both are divisible by 3 (sum of digits $1+8+9=18$, divisible by 3; sum of digits $6+5+1=12$, divisible by 3).

• $189 \div 3 = 63$
• $651 \div 3 = 217$
• New Ratio = 63 : 217

Now, let's check for other common factors. 63 is $9 \times 7$. Let's see if 217 is divisible by 7. $217 \div 7 = 31$.

• $63 \div 7 = 9$
• $217 \div 7 = 31$
• Simplified Ratio = 9 : 31

The ratio of the number of males in Organisation A to the number of males in Organisation C is 9 : 31.

Revision Table: Key Calculations

Additional Information: Understanding Percentages and Ratios in Data Interpretation

Data interpretation questions often combine different concepts like percentages, ratios, and averages. Understanding how to work with these is crucial.

• Percentages: A percentage represents a part out of a hundred. To find the value of a percentage, convert the percentage to a decimal or fraction (divide by 100) and multiply it by the total amount. For example, 18% of 35,000 is $0.18 \times 35000$ or $\frac{18}{100} \times 35000$.
• Ratios: A ratio expresses the relative size of two or more values. A ratio $A : B$ means that for every $A$ units of the first quantity, there are $B$ units of the second quantity. The total number of parts in the ratio is $A+B$. To find the actual quantity represented by a part of the ratio, divide the total amount for that category by the sum of the ratio parts and then multiply by the specific part of the ratio you are interested in. In our case, for a Male : Female ratio of 3 : 7, the total parts are 10. If there are 6300 employees in total, the number of males is $\frac{3}{10}$ of 6300.
• Combining Concepts: In this problem, we first used percentages to find the total number of employees in each organisation and then used ratios to find the specific number of males within those totals. This is a common pattern in data analysis problems. Always read the question carefully to understand what specific values are needed (e.g., number of males, females, or total employees) and from which categories (e.g., Organisation A, Organisation C, or combined).