Question

The charge for a single room at Hotel P is 25 percent less than the charge for a single room at Hotel R and 10 percent less than the charge for a single room at Hotel G. The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G ?
A. 15%
B. 20%
C. 40%
D. 50%
E.150%

Answer 1

Answer:

B. 20%

Step-by-step explanation:

Let x be the charge in hotel P,

∵ Charge in P is 25 percent less than the charge at Hotel R,

⇒ x = charge in R - 25% of charge in R = 75% of charge in R

⇒ $\frac{75}{100}\times \text{charge in R}=x$

⇒ $\frac{3}{4}\times \text{charge in R}=x$

⇒ $\text{charge in R}=\frac{4}{3}x$

Similarly, Charge in P is 10 percent less than the charge at Hotel G,

⇒ x = 90% of charge in G

⇒ $\frac{90}{100}\times \text{charge in G}=x$

⇒ $\frac{9}{10}\times \text{charge in G}=x$

⇒ $\text{charge in G}=\frac{10}{9}x$

Since,

$\frac{\frac{4}{3}x-\frac{10}{9}x}{\frac{10}{9}x}\times 100$

$=\frac{\frac{12-10}{9}}{\frac{10}{9}}\times 100$

$=\frac{\frac{2}{9}}{\frac{10}{9}}\times 100$

$=\frac{1}{5}\times 100$

$=20\%$

Hence, the charge for a single room at Hotel R is 20 percent greater than the charge for a single room at Hotel G.