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# There are 240 doctors and nurses at a hospital. If the ratio of doctor

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Joined: 02 Sep 2009
Posts: 60687
There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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16 Nov 2015, 22:52
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95% (00:42) correct 5% (01:14) wrong based on 76 sessions

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There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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17 Nov 2015, 00:14
Let number of doctors= 5x
and number of nurses = 7x
Total number of doctors and nurses = 240
5x+7x = 240
=>12x =240
=> x =20

Number of nurses =7x =7*20 = 140

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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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17 Nov 2015, 04:32
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.

There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

Let the number of doctors be D and that of nurses be N.
Then we have D+N=240, D:N=5:7.
So we have 5N=7D ---> N=7K, D=5K. 240=D+N=12K ---> K=20.
So N=140.

The answer is, therefore, (D).
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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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17 Nov 2015, 05:17
as given
The total number of Doctors and nurses =240
let number of doctors be 5x and
number of nurses be 7x
now
5x+7x=240
x=20
thus number of doctors =5*20=100 and
number of nurses =7*20=140
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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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17 Nov 2015, 10:01
Bunuel wrote:
There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

Total Number of nurses is (7/12)*240 = 140 Nurses.

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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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23 Nov 2019, 09:09
Top Contributor
Bunuel wrote:
There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

The ratio of doctors to nurses is 5 to 7
5 + 7 = 12.
So we can say that, for every 12 workers, 5 are doctors and 7 are nurses.
In other words, 7/12 of the workers are nurses.

We are told that there are 240 workers in total
So, the total number of nurses = 7/12 of 240
= (7/12)(240)
= 140

Cheers,
Brent
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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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23 Nov 2019, 09:16
We can solve this question by just looking at the answers.

The ratio of doctors to nurse is 5 to 7 ==> D:N = 5x:7x ==> the number of nurses is a multiple of 7 ==> answer is D since it is the only multiple of 7 in the answer choices.
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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor  [#permalink]

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12 Dec 2019, 19:54
Bunuel wrote:
There are 240 doctors and nurses at a hospital. If the ratio of doctors to nurses is 5 to 7, how many nurses are at the hospital?

A. 20
B. 60
C. 100
D. 140
E. 180

We can create the equation:

240 = 5x + 7x

240 = 12x

20 = x

So there are 7 * 20 = 140 nurses.

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Re: There are 240 doctors and nurses at a hospital. If the ratio of doctor   [#permalink] 12 Dec 2019, 19:54
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