In a market research project, 20% opted for Nirma detergent whereas 60% opted for Surf Blue detergent. The remaining individuals were not certain. If the difference between those who opted for Surf Blue and those who were uncertain was 720, how many respondents were covered in the survey?

Concept & Logic The total percentage of respondents must equal $100\%$. Find the percentage for the uncertain group, then equate the given numerical difference to its corresponding percentage difference to find the total. $$ \text{Total Respondents} = \frac{\text{Given Difference}}{\text{Percentage Difference}} $$ Step-by-Step Solution * Given: Nirma = $20\%$, Surf Blue = $60\%$. * Calculate the percentage of uncertain individuals: $100\% - (20\% + 60\%) = 100\% - 80\% = 20\%$. * Given: The numerical difference between Surf Blue and Uncertain is $720$. * Calculate the percentage difference between Surf Blue and Uncertain: $60\% - 20\% = 40\%$. * Set up the equation: $40\%$ of Total Respondents = $720$. * Total Respondents = $\frac{720}{40\%} = \frac{720}{0.40} = 1800$. Exam Strategy & Shortcut Difference in percentage is $60\% - 20\% = 40\%$. $40\%$ corresponds to $720$. To find $100\%$, you can use a multiplier. $40\% \times 2.5 = 100\%$. Therefore, $720 \times 2.5 = 1800$. Common Pitfall Calculating the difference between Nirma and Surf Blue ($40\%$) by misreading the question, instead of Surf Blue and the Uncertain group. Read the specific comparison groups carefully. Final Answer Therefore, the correct answer is **1800**.