Question

In a certain town$30\%$ families own a scooter and $40\%$ own a car,$50\%$ own neither a scooter nor a car. $2000$families own both a scooter and car consider the following statements in this regard

1)$20\%$ of families own both scooters and cars.

2) $35\%$ of families own either a car or a scooter.

3)$10000$ families live in town.

Which of the above statement are correct?

• A. $2$ and $3$
• B. $1,2$ and $3$
• C. $1$ and $2$
• D. $1$ and $3$

Answer 1

The correct option is D

$1$ and $3$

Explanation for the correct option:

Let there be $\mathrm{x}$ families that live in the town then,

$A$ be the families have scooter.

$B$ be the families have car.

$\begin{array}{rcl}\mathrm{n}\left(\mathrm{A}\right)& =& \frac{30\mathrm{x}}{100}\\ \mathrm{n}\left(\mathrm{B}\right)& =& \frac{40\mathrm{x}}{100}\\ \mathrm{n}\left(\mathrm{AUB}\right)\text{'}& =& \frac{50\mathrm{x}}{100}\\ \mathrm{n}\left(\mathrm{AUB}\right)& =& \frac{50\mathrm{x}}{100}\mathbf{[}\mathbf{\because }\mathbf{}\mathbf{n}\mathbf{\left(}\mathbf{A}\mathbf{\right)}\mathbf{+}\mathbf{n}{\mathbf{\left(}\mathbf{A}\mathbf{\right)}}^{\mathbf{\text{'}}}\mathbf{=}\mathbf{x}\mathbf{]}\\ \mathrm{n}(\mathrm{A}\cap \mathrm{B})& =& \frac{20\mathrm{x}}{100}\\ \frac{20\mathrm{x}}{100}& =& 2000\mathbf{\left[}\mathbf{given}\mathbf{\right]}\\ \mathrm{x}& =& 10000\\ & & \end{array}$

Percentage of people with both scooter and car is $20\%$.

Hence, the correct option is D.