In an area, of the total people 40% were women and 45% coffee drinkers. One-third of the males are coffee drinkers. Suppose the total number of persons in the area is 100, then the number of female non-coffee drinkers is

### Concept & Logic Use a matrix or a structured breakdown (like a Venn diagram logic) to categorize the population based on two overlapping binary traits: Gender (Male/Female) and Preference (Coffee/No Coffee). ### Step-by-Step Solution * **Given:** Total population = 100. Women = 40%. Total coffee drinkers = 45%. $\frac{1}{3}$ of males drink coffee. * **Calculation / Deduction:** * Since the total number of people is 100, the percentages translate directly to exact numbers. * Number of women = 40. * Number of men = $100 - 40 = 60$. * Total coffee drinkers = 45. * Calculate the number of male coffee drinkers: $$ \text{Male Coffee Drinkers} = \frac{1}{3} \times 60 = 20 $$ * Use the total coffee drinkers to find the female coffee drinkers: $$ \text{Female Coffee Drinkers} = \text{Total Coffee Drinkers} - \text{Male Coffee Drinkers} $$ $$ \text{Female Coffee Drinkers} = 45 - 20 = 25 $$ * Finally, find the number of female non-coffee drinkers by subtracting the female coffee drinkers from the total women: $$ \text{Female Non-Coffee Drinkers} = \text{Total Women} - \text{Female Coffee Drinkers} $$ $$ \text{Female Non-Coffee Drinkers} = 40 - 25 = 15 $$ ### Exam Strategy & Shortcut **Grid Mapping (Tabular Method):** Draw a quick $2 \times 2$ grid. | | Coffee | No Coffee | Total | | :--- | :---: | :---: | :---: | | **Men** | 20 | | 60 | | **Women** | 25 | **15** | 40 | | **Total** | 45 | | 100 | Once you fill in the bold given numbers (100 total, 40 women, 60 men, 45 total coffee), and calculate the $60 \div 3 = 20$ male coffee drinkers, the rest of the table solves itself through simple subtraction. $40 - 25 = 15$. ### Common Pitfall A common mistake is applying the $\frac{1}{3}$ multiplier to the *total coffee drinkers* rather than the *total males*. Always read carefully to see which subgroup the fraction or percentage modifies. ### Final Answer **Therefore, the correct answer is 15.**