Directions: Study the following table carefully and answer the questions that follow: Number of Candidates (in lakhs) Appearing In an Entrance Examination From Six Different Cities | City | A | B | C | D | E | F | | :--- | :--- | :--- | :--- | :--- | :--- | :--- | | **Number of candidates** | 1.25 | 3.14 | 1.08 | 2.27 | 1.85 | 2.73 | Ratio of Candidates Passing And Failing Within the City | City | Ratio of Passing and Failing | | :--- | :--- | | **A** | 7 : 3 | | **B** | 5 : 3 | | **C** | 4 : 5 | | **D** | 1 : 3 | | **E** | 3 : 2 | | **F** | 7 : 5 | Which city has the highest number of students failing the entrance exam ?

### Concept & Strategy To determine which city has the highest absolute number of failing students, we must calculate the failing candidates for each city by multiplying the total appearing candidates by the failing fraction for that city. The failing fraction is $\frac{\text{Failing Ratio}}{\text{Total Ratio}}$. ### Step-by-Step Solution Let's compute the failing candidates (in lakhs) for the cities provided in the options and potentially others to be safe: 1. **City A:** $1.25 \times \frac{3}{10} = 0.375$ 2. **City B:** $3.14 \times \frac{3}{8} = 1.1775$ 3. **City C:** $1.08 \times \frac{5}{9} = 0.60$ 4. **City D:** $2.27 \times \frac{3}{4} = 1.7025$ 5. **City E:** $1.85 \times \frac{2}{5} = 0.74$ 6. **City F:** $2.73 \times \frac{5}{12} \approx 2.73 \times 0.416 \approx 1.1375$ Comparing all values: - A: $0.375$ - B: $1.1775$ - C: $0.60$ - D: $1.7025$ - E: $0.74$ - F: $1.1375$ The highest value is $1.7025$ lakhs, which belongs to City D. ### Exam Strategy & Shortcut You can often identify the highest without exact calculations by looking for a combination of a high total population and a high failing fraction. City D has a huge failing ratio of $3$ out of $4$ ($75\%$). $75\%$ of $2.27$ is obviously quite large. City B has a high population ($3.14$) but its failing fraction is only $3/8$ ($37.5\%$). $37.5\%$ of $3.14$ is slightly more than $1$. City D ($75\%$ of $2.27$) is clearly closer to $1.7$. Visual inspection quickly narrows the race down to B and D, and a rough estimation proves D is the winner. ### Common Pitfall A typical trap is assuming that the city with the largest total population (City B) will naturally have the most failing students. You must always account for the specific passing/failing ratio of that city. ### Final Answer Therefore, the correct answer is **D**.