To solve the problem, we need to understand the concept of inverse proportionality. When we say that one quantity is inversely proportional to another, it means that as one quantity increases, the other decreases, and vice versa. Mathematically, we can express this relationship as: \[ L = \frac{k}{W} \] Where: - \( L \) is the length a person can jump, - \( W \) is the weight of the person, - \( k \) is the constant of proportionality. ### Step-by-Step Explanation 1. **Identify the Variables**: - From the problem, we know: - The weight \( W = 20 \) kg - The jump length \( L = 1.5 \) m 2. **Set Up the Equation**: - Using the formula for inverse proportionality, we can substitute the known values into the equation: \[ 1.5 = \frac{k}{20} \] 3. **Solve for the Constant \( k \)**: - To find \( k \), we can rearrange the equation: \[ k = 1.5 \times 20 \] - Now, perform the multiplication: \[ k = 30 \] 4. **Conclusion**: - The constant of proportionality \( k \) is 30. ### Explanation of the Options Now, let's evaluate the options provided: - **A. 60**: This option is incorrect because if \( k \) were 60, then substituting back into the equation would give a jump length of \( \frac{60}{20} = 3 \) m, which contradicts the given information. - **B. 30**: This is the correct option. As we calculated, substituting \( k = 30 \) gives us the correct jump length of 1.5 m when the weight is 20 kg. - **C. 20**: This option is incorrect. If \( k \) were 20, then the jump length would be \( \frac{20}{20} = 1 \) m, which is not consistent with the given jump length of 1.5 m. - **D. 15**: This option is also incorrect. If \( k \) were 15, then the jump length would be \( \frac{15}{20} = 0.75 \) m, which is far less than the given jump length. ### Summary of Key Points - The relationship between jump length and weight is inversely proportional. - The formula used is \( L = \frac{k}{W} \). - By substituting the known values, we found \( k = 30 \). - The correct answer is **B. 30**. ### Revision Summary - Inverse proportionality means one quantity increases as the other decreases. - The formula for inverse proportionality is \( L = \frac{k}{W} \). - To find the constant of proportionality, rearrange the formula and substitute known values. - Always check each option by substituting back into the original relationship to verify correctness.