The number of students in two sections A and B having different heights is shown in the table given below. | Height (in metres) | Section A | Section B | | :--- | :--- | :--- | | 1.55 | 3 | 2 | | 1.60 | 7 | 6 | | 1.62 | 12 | 14 | | 1.65 | 15 | 14 | | 1.68 | 8 | 9 | | 1.71 | 6 | 5 | | 1.75 | 3 | 4 | The ratio of the number of students of a particular height in section A to that in section B is the maximum for the height of

### Concept & Comparing Ratios To find the maximum ratio of students in Section A to Section B for a given height, we simply need to divide the number of students in Section A by the number of students in Section B for each corresponding row in the table, and then compare the resulting decimal values or fractions. $$ \text{Ratio} = \frac{\text{Students in Section A}}{\text{Students in Section B}} $$ ### Step-by-Step Solution 1. We need to check the ratios for the specific heights provided in the options, or ideally, all of them to be certain. Let's calculate the ratio $\frac{A}{B}$ for each height given in the options: 2. For $1.55$ m: Ratio = $\frac{3}{2} = 1.5$ 3. For $1.60$ m: Ratio = $\frac{7}{6} \approx 1.166$ 4. For $1.65$ m: Ratio = $\frac{15}{14} \approx 1.071$ 5. For $1.71$ m: Ratio = $\frac{6}{5} = 1.2$ 6. Checking the other heights for safety (though not in the options): * $1.62$ m: $\frac{12}{14} \approx 0.85$ (less than $1$) * $1.68$ m: $\frac{8}{9} \approx 0.88$ (less than $1$) * $1.75$ m: $\frac{3}{4} = 0.75$ (less than $1$) 7. Comparing all the ratios, the maximum value is $1.5$, which occurs at the height of $1.55$ m. ### Exam Strategy & Shortcut You don't need to calculate the exact decimals for every fraction. First, eliminate any fractions where the numerator is smaller than the denominator (since their ratio is $< 1$). This eliminates heights $1.62$, $1.68$, and $1.75$. Next, visually compare the remaining fractions: $\frac{3}{2}$, $\frac{7}{6}$, $\frac{15}{14}$, and $\frac{6}{5}$. $\frac{3}{2}$ is $1 \frac{1}{2}$, while the others are $1$ and a fraction much smaller than a half ($\frac{1}{6}$, $\frac{1}{14}$, $\frac{1}{5}$). Thus, $\frac{3}{2}$ is clearly the largest. ### Common Pitfall A potential trap is to calculate the inverse ratio (Section B to Section A) or to mistake the absolute difference for the ratio. Always strictly calculate exactly what is requested: $\frac{\text{Section A}}{\text{Section B}}$. ### Final Answer Therefore, the correct answer is **1.55 m**.