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In a hair cut competition, the number of blonde girls is three times

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In a hair cut competition, the number of blonde girls is three times  [#permalink]

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New post 17 Sep 2019, 00:11
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A
B
C
D
E

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Question Stats:

78% (01:34) correct 22% (01:41) wrong based on 37 sessions

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In a hair cut competition, the number of blonde girls is three times bigger than the number of brown haired girls, and the number of brown haired girls is twice the number of red haired girls. Assuming that there is no other hair color, what is the proportion of the brown haired girls?

A. 2/3.
B. 4/9.
C. 1/3.
D. 5/9.
E. 2/9.

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Re: In a hair cut competition, the number of blonde girls is three times  [#permalink]

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New post 17 Sep 2019, 00:20
Let \(x\)=Number of Blonde girls
\(y\)=Number of Brown haired girls
\(z\)=Number of Red Haired girls

Given,

\(x=3y, y=2z\) or \(z=\frac{y}{2}\)

To find,

\(\frac{y}{x+y+z}\)

Substituting for \(x\) & \(z\),

\(\frac{y}{3y+y+y/2} = \frac{2}{9}\)

Answer is (E)
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Re: In a hair cut competition, the number of blonde girls is three times  [#permalink]

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New post 17 Sep 2019, 02:56
Bunuel wrote:
In a hair cut competition, the number of blonde girls is three times bigger than the number of brown haired girls, and the number of brown haired girls is twice the number of red haired girls. Assuming that there is no other hair color, what is the proportion of the brown haired girls?

A. 2/3.
B. 4/9.
C. 1/3.
D. 5/9.
E. 2/9.


blonde=3 brown
brown=2 red
let red= 4 ; brown =8 and blonde =24
total 36
brown hair proportion ; 8/36 ; 2/9
IMO E
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Re: In a hair cut competition, the number of blonde girls is three times  [#permalink]

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New post 17 Sep 2019, 07:58
Bunuel wrote:
In a hair cut competition, the number of blonde girls is three times bigger than the number of brown haired girls, and the number of brown haired girls is twice the number of red haired girls. Assuming that there is no other hair color, what is the proportion of the brown haired girls?

A. 2/3.
B. 4/9.
C. 1/3.
D. 5/9.
E. 2/9.

Let, No of Red haired Girl be = 1 , So, Brown haired Girls = 2 and No of blonde girls = 6 , Total No of Girls = 9

So, proportion of the brown haired girls is 2/9 , Answer must be (E)
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Re: In a hair cut competition, the number of blonde girls is three times  [#permalink]

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New post 21 Sep 2019, 12:25
Bunuel wrote:
In a hair cut competition, the number of blonde girls is three times bigger than the number of brown haired girls, and the number of brown haired girls is twice the number of red haired girls. Assuming that there is no other hair color, what is the proportion of the brown haired girls?

A. 2/3.
B. 4/9.
C. 1/3.
D. 5/9.
E. 2/9.


We can let D = the number of blonde girls, W = the number of brown haired girls, and R = the number of red haired girls. We can create the equations:

D = 3W

and

W = 2R

W/2 = R

The proportion of brown haired girls is:

W/(W + 3W + W/2)

Multiplying by 2/2, we have:

2W/(2W + 6W + W) = 2W/9W = 2/9

Answer: E
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Re: In a hair cut competition, the number of blonde girls is three times   [#permalink] 21 Sep 2019, 12:25
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