In a group there are 24 men and 26 women. Find: (a) the percentage of men in the group.(b) the percentage of women in the group.
The Correct Answer and Explanation is:
To solve this problem, we need to determine the percentage of men and women in a group consisting of 24 men and 26 women.
(a) Percentage of Men in the Group
Step 1: Find the total number of people in the group. Total people=24 (men)+26 (women)=50\text{Total people} = 24\ (\text{men}) + 26\ (\text{women}) = 50
Step 2: Calculate the percentage of men: Percentage of men=(2450)×100=48%\text{Percentage of men} = \left(\frac{24}{50}\right) \times 100 = 48\%
(b) Percentage of Women in the Group
Step 1: The number of women is 26.
Step 2: Calculate the percentage of women: Percentage of women=(2650)×100=52%\text{Percentage of women} = \left(\frac{26}{50}\right) \times 100 = 52\%
Explanation
In any group or population, percentages are used to express the proportion of a part relative to the whole. This problem involves a basic percentage calculation based on a group of 50 people consisting of 24 men and 26 women.
To find a percentage, the standard formula is: Percentage=(PartWhole)×100\text{Percentage} = \left(\frac{\text{Part}}{\text{Whole}}\right) \times 100
Applying this to the men, we take 24 (the number of men) and divide it by the total group size of 50. Multiplying the resulting fraction by 100 gives us 48%. This means that out of every 100 people in this group, 48 would be men if the group were scaled up proportionally.
Similarly, for the women, we divide 26 (the number of women) by the total of 50 and multiply by 100. The result is 52%, showing that slightly more than half of the group consists of women.
These calculations also serve as a good check: if we add the percentage of men (48%) and women (52%), the total is 100%, confirming the accuracy of the values. This is a basic principle in percentage problems—if you’re accounting for all parts of a whole, their percentages must sum to 100%.
This kind of problem is useful in everyday life—whether analyzing survey results, demographics, or budgeting—because it transforms raw numbers into easily understandable proportions, helping in decision-making, comparisons, and visual representation.
