## The charge for a single room at Hotel $$P$$ is $$25$$ percent less than the charge for a single room at Hotel $$R$$ and

##### This topic has expert replies
Legendary Member
Posts: 2184
Joined: 07 Sep 2017
Thanked: 6 times
Followed by:4 members

### The charge for a single room at Hotel $$P$$ is $$25$$ percent less than the charge for a single room at Hotel $$R$$ and

by Vincen » Wed Mar 31, 2021 7:33 am

00:00

A

B

C

D

E

## Global Stats

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.$$150\%$$

Source: GMAT Prep

### GMAT/MBA Expert

GMAT Instructor
Posts: 6195
Joined: 25 Apr 2015
Location: Los Angeles, CA
Thanked: 43 times
Followed by:24 members

### Re: The charge for a single room at Hotel $$P$$ is $$25$$ percent less than the charge for a single room at Hotel $$R$$

by [email protected] » Thu Apr 15, 2021 10:33 am
Vincen wrote:
Wed Mar 31, 2021 7:33 am
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.$$150\%$$

Solution:

We can let the charge for a room at hotel P = p, the charge for a room at hotel G = g, and the charge for a room at hotel R = r.

We are given that 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. Thus:

p = 0.75r

And

p = 0.9g

Since both right-hand expressions are equal to p, we set them equal to each other, and then we solve for r.

0.75r = 0.9g

r = 1.2g

Thus, Hotel R’s rate is 20% greater than Hotel G’s rate.