Question

In a certain town,$25\%$ of families own a cell phone, $15\%$ of families own a scooter and $65\%$ of families own neither a cell phone nor a scooter. If $1500$families own both a cell phone and a scooter, then the total number of families in the town is

• A. $10000$
• B. $20000$
• C. $30000$
• D. $40000$
• E. $50000$

Answer 1

The correct option is C

$30000$

Explanation for the correct option:
Finding the total number of families in a town:

Given that,

The percentage of families that own a cell phone$=25\%$

The percentage of families that own a scooter $=15\%$

The percentage of families that own neither a cell phone nor a scooter$=65\%$

Now, let the number of families in the town is be $x$.

$$\begin{gathered} \frac{25\mathrm{x}}{100}+\frac{15\mathrm{x}}{100}-1500+\frac{65\mathrm{x}}{100}=\mathrm{x} \\ \Rightarrow \frac{105\mathrm{x}}{100}-\mathrm{x}=1500 \\ \Rightarrow \frac{5\mathrm{x}}{100}=1500 \\ \Rightarrow \mathrm{x}=30000 \end{gathered}$$

Hence, the correct option is C.