In a certain town 25 % families own a cell phone, 15 % families own a scooter and 65 % 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

Question

In a certain town 25 % families own a cell phone, 15 % families own a scooter and 65 % 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) 10,000 (B) 20,000 (C) 30,000 (D) 40,000

Tardigrade Admin · Accepted Answer

Let the total population of town be x . ∴ (25x/100)+(15x/100)-1500+(65x/100)=x ⇒ (105x/100)-x=1500 ⇒ (5x/100)=1500 ⇒ x=30000

Q. In a certain town $25%$ families own a cell phone, $15%$ families own a scooter and $65%$ 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

$10, 000$

$20, 000$

$30, 000$

$40, 000$

$50, 000$

Let the total population of town be $x$ .

$∴$ $\frac{25 x}{100} + \frac{15 x}{100} - 1500 + \frac{65 x}{100} = x$
$\Rightarrow$ $\frac{105 x}{100} - x = 1500$
$\Rightarrow$ $\frac{5 x}{100} = 1500$
$\Rightarrow$ $x = 30000$

Q. In a certain town 25% families own a cell phone, 15% families own a scooter and 65% 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

10,000

20,000

30,000

40,000

50,000

Let the total population of town be x . ∴ 10025x​+10015x​−1500+10065x​=x ⇒ 100105x​−x=1500 ⇒ 1005x​=1500 ⇒ x=30000