Question

15. 65% of the area of a city is covered by house. If the
area left off is 3(1÷2)sq. miles, find the area of the whole
city.
A) 9.50 sq. miles
B) 10.00 sq. miles
C) 8.50 sq. miles
D) 7.5 sq. miles​

Answer 1

$\LARGE{\bf{\underline{\underline{GIVEN:-}}}}$

• 65% of the area is covered with houses.
• The area left is $\sf 3\frac{1}{2}$ square miles ⇒ $\frac{7}{2}$ square miles (Convert proper fraction into an improper fraction.

$\LARGE{\bf{\underline{\underline{TO:FIND:-}}}}$

• The total area of city.

$\LARGE{\bf{\underline{\underline{SOLUTION:-}}}}$

Let the total area of the city be x sq. miles.

65% of the city is covered. Therefore, area of the city that is covered:

$\to \sf 65 \% \ of \ x$

$\to \sf \dfrac{65 x}{100}$

$\sf \to \dfrac{13x}{20}$

But we know that the area left is $\frac{7}{2}$. Therefore, we can conclude that:

Area covered + Area left = Total area.

$\sf \to \dfrac{13x}{20}+\dfrac{7}{2} = x$

$\sf \to \dfrac{7}{2} =x-\dfrac{13x}{20}$

$\sf \to \dfrac{7}{2} =\dfrac{7x}{20}$

$\sf \to x=\dfrac{\not{7}}{2} \times \dfrac{20}{\not{7} }$

$\boxed{\sf{\green{x=10 sq. \ miles}}}$

OPTION B IS CORRECT.

Answer 2

Answer:

Above solution is correct