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?

Answer 1

Answer:

16.67 % ( approx )

Step-by-step explanation:

Let x be the charge at hotel P,

Since, the charge at Hotel P is 25 percent less than the charge at Hotel R,

That is, (100-25)% of charge at hotel R = charge at hotel P

75% of charge at hotel R = x

⇒ Charge at hotel R = $\frac{100x}{75}$ = $\frac{4x}{3}$,

The charge at Hotel P is 10 percent less than the charge at Hotel G

(100-10)% of charge at hotel G = charge at hotel P

90% of charge at hotel G = x

⇒ Charge at hotel G = $\frac{100 x}{90}$ = $\frac{10x}{9}$,

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

$=\frac{\frac{12x-10x}{9}}{\frac{4x}{3}}\times 100$

$=\frac{\frac{2x}{9}}{\frac{4x}{3}}\times 100$

$=\frac{1}{6}\times 100$

$=\frac{100}{6}$

$\approx 16.67\%$

Hence, the charge for a single room at Hotel R is approximately 16.67 % greater than the charge for a single room at Hotel G.