Question

In a market survey, 20% opted for product A whereas 60% opted for product B. The remaining individuals were not certain. If the difference between those who opted for product B and those who were uncertain was 720, how many individuals were covered in the survey?

Answer 1

Hint: Assume the total number of individuals as some variable. Generate equations from the given information and solve them to get the required answer.

Complete step-by-step answer:

Let us assume the total number of individuals covered in the survey was x. It is given that 20% of x opted for product A whereas 60% of x opted for product B.
So, number of people opted for product A = \[x\cdot \dfrac{20}{100}=\dfrac{x}{5}\] and number of people opted for product B is = \[x\cdot \dfrac{60}{100}=\dfrac{3x}{5}\].
So, remaining number of individuals those who were uncertain is = \[x-\left( \dfrac{x}{5}+\dfrac{3x}{5} \right)\] = \[\dfrac{x}{5}\]
Now it is given that the difference between those who opted for product B and those who were uncertain was 720. Therefore, we can write in equation as \[\dfrac{3x}{5}-\dfrac{x}{5}=720\]
\[\Rightarrow \dfrac{2x}{5}=720\]
Or,\[x=\dfrac{5\cdot 720}{2}\] = 1800
Therefore, this is the total number of individuals in that survey.
Hence, there were a total 1800 individuals covered in that survey.

Note: As the number of individuals opting for product A or B or uncertain in that case are independent in numbers we can solve this problem by above method. There were no people who opted for both at least two of them. If it were so then we would use set theory methods.