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

B. 20%

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

⇒
`(75)/(100)* \text{charge in R}=x`

⇒
`(3)/(4)* \text{charge in R}=x`

⇒
`\text{charge in R}=(4)/(3)x`

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

⇒ x = 90% of charge in G

⇒
`(90)/(100)* \text{charge in G}=x`

⇒
`(9)/(10)* \text{charge in G}=x`

⇒
`\text{charge in G}=(10)/(9)x`

Since,

`((4)/(3)x-(10)/(9)x)/((10)/(9)x)* 100`

`=((12-10)/(9))/((10)/(9))* 100`

`=((2)/(9))/((10)/(9))* 100`

`=(1)/(5)* 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.