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The charge for a single room at Hotel P is 25 percent less

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The charge for a single room at Hotel P is 25 percent less [#permalink]

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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%

[Reveal] Spoiler:
I solved the the problem as follows:
Let rate in R = 100x
then P = 75x

G = 100y
P = 90y

Thus
75x=90y
or x = 1.20 y
Ans R = 120y
so increase = 20%

But I tried first to solve the problem as follows:
p = 100
R = 120
G = 110
and Failed Please help on my second effort.
[Reveal] Spoiler: OA

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Originally posted by Baten80 on 20 Jan 2012, 13:54.
Last edited by abhimahna on 19 Sep 2017, 06:31, edited 1 time in total.
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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New post 20 Jan 2012, 14:26
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Baten80 wrote:
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%

I solved the the problem as follows:
Let rate in R = 100x
then P = 75x

G = 100y
P = 90y

Thus
75x=90y
or x = 1.20 y
Ans R = 120y
so increase = 20%

But I tried first to solve the problem as follows:
p = 100
R = 120
G = 110
and Failed Please help on my second effort.


As everything is linked with P then: \(0.75R=P=0.9G\) --> \(75R=90G\) --> \(\frac{R}{G}=\frac{90}{75}=1.2\).

Answer: B.

As for your second approach. The numbers are incorrect:
If R=120 then P=90 (not 100);
If G=110 then P=99 (not 100);
If P=100 then R=100/0.75=~133.3 and G=100/0.9=~111.1.
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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This is a example of Combined Ratios since we need to compare one thing which is common to two other things separately.
Lets consider that charge for Hotel R is $100 then the charge for Hotel P becomes $ 75 (100-75). Similarly considering the charge for Hotel G as $100 the charge for Hotel becomes $ 90 (100-10).
Reducing it to ratios P:R:=75:100 i.e. P:R:=3:4
Similarly P:G:=90:100 i.e. P:G:=9:10
We cannot instantly combine these ratios into a single ratio since the terms for P are different.
So we need to convert these two ratios to combined ration by multiplying first ration with 3 which then becomes 9:12.
Hence the combined ration becomes P:R:G:=9:12:10 which implies that the ratio for R:G is 12:10
So if the charge at Hotel G is $100 then charge at Hotel R becomes $120 or in other words 20% higher.
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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Answer = B 20%

Please refer below:
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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P = (3/4) R = (9/10) G => R=(6/5) G => R= G+(1/5) G => 20%
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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New post 02 Apr 2015, 19:28
This is how I solved it. Please correct me if I am wrong.
Let R = 100

P= 100*.75= 75 (P is 25% less than R)
G = 75(P) * 1.10 = 82.5 ( G is 10% more than P)

R/G = 100/82.5 = 1.21% Therefore R is 20% greater than G

Alternatively

I can do G/R = 82.5/100 = 82.5% - 1 = 17.5% R is 17.5% greater than G. Looking at choices, I would pick 20%
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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I saw this question at the very end of a GMAC practice test and I had like 30 seconds to do it so this was the fastest way I could come up with:

P=(3/4)R
p=(9/10)G

(9/10)G=(3/4)R
12/10G=R
12/10=20% greater Answer B

Originally posted by DJ1986 on 21 Nov 2015, 18:15.
Last edited by DJ1986 on 25 Feb 2016, 16:23, edited 1 time in total.
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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Hi All,

This question can be solved by TESTing VALUES.

Let's TEST...
The single room charge at Hotel R = $100
The single room charge at Hotel P = $75
The single room charge at Hotel G = about $83

This question uses the phrase "what percent greater…" which means that we have to use the Percentage Change Formula:

Percentage Change = (New - Old)/Old.

In this scenario, the price at Hotel R is the "New" number and the price at Hotel G is the "Old" number.

Using the numbers we're TESTing, we have…

(100 - 83)/83 = 17/83

Since we estimated that "83", the correct answer will be approximately...

17/85 = 1/5 = 20%

Final Answer:
[Reveal] Spoiler:
B


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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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New post 30 Nov 2016, 11:30
Baten80 wrote:
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%


Let \(p\) = \(\frac{3r}{4}\) = \(\frac{9g}{10}\) = \(90\)

So, \(p = 90\) ; \(r = 120\) & \(g = 100\)

Quote:
The charge for a single room at Hotel R is what percent greater than the charge for a single room at Hotel G


\(\frac{120 - 100}{100}*100 = 20\) %

Hence, answer will be (B) 20 %
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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New post 06 May 2017, 10:20
Hi Bunuel ,

Thanks for the Clear and crisp explanation. :)

Warm Regards,
Kritesh Singh
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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New post 06 May 2017, 20:44
I've considered P=100(as everything is based on P)
Thus R = 125 and G = 110
% change = (125-110)/125=12
Not sure where am I going wrong. Kindly explain.
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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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Hi umadurga,

You have to be very careful here - especially when dealing with percent change.

To start, the number 100 is NOT "25% less" than 125... it's only 20% less. Since 125 is the 'base' number, you would have to subtract (25% of 125) from 125... and that would not be a 'nice' number (it would be 125 - 31.25 = 93.75).

If you read my post (a few posts up the page from your post), you'll see how you can make R=100 and proceed from there with relatively nice values.

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Re: The charge for a single room at Hotel P is 25 percent less [#permalink]

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New post 07 Dec 2017, 17:54
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Baten80 wrote:
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%


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

p = 3r/4

AND

p = 0.9g

p = 9g/10

We need to determine what percent greater the charge is for hotel R than for hotel G. Thus, we need to evaluate (r - g)/g x 100. However, we first need to get variables r and g in terms of p.

r = 4p/3

AND

g = 10p/9

Substitute 4p/3 for r and 10p/9 for g and we have:

(r - g)/g x 100

[(4p/3 - 10p/9)/(10p/9)] x 100

[(12p/9 - 10p/9)/(10p/9)] x 100

[(2p/9)/(10p/9)] x 100

2/10 x 100 = 20 percent

Alternate 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 = .75r

And

p = .9g

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

.75r = .9g

r = 1.2g

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

Answer: B
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Re: The charge for a single room at Hotel P is 25 percent less   [#permalink] 07 Dec 2017, 17:54
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