Please help with this...
On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?
(A) $600
(B) $800
(C) $1000
(D) $1600
(E) $2400
GMAT past paper - Algebra / Range
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Let the actual rent motel charged for the night = x
Ten $60 rooms were rented for $40, so the rent didn't charge =
(60-40)x10 = 200
If all the rooms were to be charged for their actual price, rent collected
would have been = x+200
Total rent the motel charged was reduced by 25 percent, Or,
actual rent charged was 75% of the rent, if all rooms were rented for actual price.
x = (75/100)(x+200)
Or, x = 600. Choice A
Ten $60 rooms were rented for $40, so the rent didn't charge =
(60-40)x10 = 200
If all the rooms were to be charged for their actual price, rent collected
would have been = x+200
Total rent the motel charged was reduced by 25 percent, Or,
actual rent charged was 75% of the rent, if all rooms were rented for actual price.
x = (75/100)(x+200)
Or, x = 600. Choice A
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akay wrote:Please help with this...
On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?
(A) $600
(B) $800
(C) $1000
(D) $1600
(E) $2400
I am agree with Hopefully. The explanation is like -
Suppose,
60$ room = x; 40$ room = y
That night's income = 60x+40y
But according to the condition,
[{60x + 40y - {(60(x - 10) + 40(y + 10)}]/(60x + 40y)}] * 100 = 25
So 60x + 40y = 800
Correct me If I am wrong
Regards,
Amitava
Regards,
Amitava
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Let rent collected by hotel on every day basis be x
so rent collected that night would be x - 200 (20 * 10 rooms)
so Q say this 25 % less than normal rent i.e 75 % of normal rent
so x -200 = (75/100) * x
solving we get x =800
Q ask rent collected that night i.e x-200 =600
So and should be 600 A
so rent collected that night would be x - 200 (20 * 10 rooms)
so Q say this 25 % less than normal rent i.e 75 % of normal rent
so x -200 = (75/100) * x
solving we get x =800
Q ask rent collected that night i.e x-200 =600
So and should be 600 A
Regards
Samir
Samir
- gabriel
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quite a lot of discussion over here .. seems like a pretty straightforward question...akay wrote:Please help with this...
On a Saturday night, each of the rooms at a certain motel was rented for either $40 or $60. If 10 of the rooms that were rented for $60 had instead been rented for $40, then the total rent the motel charged for that night would have been reduced by 25 percent. What was the total rent the motel actually charged for that night?
(A) $600
(B) $800
(C) $1000
(D) $1600
(E) $2400
Let the total number of rooms charged at 40$ be "a" and that charged at 60$ be "b"..
.. So the total rent for that night = 40*a + 60* b ..
..Now according to the condition given the number of rooms charged at 40$ is " a+10" and that charged at 60$ is "b-10" ..
.. so the total rent in this case = 40*(a+10)+60*(b-10) .. now we know that this value is 75% of the original value ..
..So, we have 40*a+60*b=3/4(40*(a+10)+60*(b-10))..
.. 3(40*a+60*b)=4( 40*a+60*b +400-600)..
solving the 2 sides and we get 40a+60b= 800 .. which is the rent for that night ..
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actually the answer should end over here .samirpandeyit62 wrote:Let rent collected by hotel on every day basis be x
so rent collected that night would be x - 200 (20 * 10 rooms)
so Q say this 25 % less than normal rent i.e 75 % of normal rent
so x -200 = (75/100) * x
solving we get x =800
samirpandeyit62 wrote: Q ask rent collected that night i.e x-200 =600
So and should be 600 A
This is just the "if" part not what actually happened ...
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