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In a survey among students, it was found that 48% preferred coffee, 54

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In a survey among students, it was found that 48% preferred coffee, 54  [#permalink]

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New post 03 Nov 2019, 02:37
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In a survey among students, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee ans tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then, the ratio of number of students who like only coffee to the number who like only tea is

A. 5:3
B. 8:9
C. 2:3
D. 3:2
E. None of these


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Re: In a survey among students, it was found that 48% preferred coffee, 54  [#permalink]

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New post 03 Nov 2019, 03:15
1
x are those who prefer all three.
100-6= 48+54+64-28-32-30+x
x=18

Students who like Only coffee= 48-28-30+18=8

Students who like Only tea= 54- 28-32+18=12

Ratio= 8/12=2/3


Bunuel wrote:
In a survey among students, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee ans tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then, the ratio of number of students who like only coffee to the number who like only tea is

A. 5:3
B. 8:9
C. 2:3
D. 3:2
E. None of these


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Re: In a survey among students, it was found that 48% preferred coffee, 54  [#permalink]

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New post 03 Nov 2019, 03:28
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Bunuel wrote:
In a survey among students, it was found that 48% preferred coffee, 54% liked tea and 64% smoked. Of the total, 28% liked coffee ans tea, 32% smoked and drank tea and 30% smoked and drank coffee. Only 6% did none of these. If the total number of students is 2000 then, the ratio of number of students who like only coffee to the number who like only tea is

A. 5:3
B. 8:9
C. 2:3
D. 3:2
E. None of these


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Let number of people who like Coffee, Tea & Smoke be C, T & S respectively.
Let the number of people who like all the 3 = X
As per the below Venn diagram,
Image

Formula: Total(%) = '0' Category + C + T + S - (Exactly 2 category) - 2(Exactly 3 Category)
--> 100 = 6 + 48 + 54 + 64 - (28 - X + 30 - X + 32 - X) - 2X
--> 100 = 6 + 166 - 90 + X
--> 100 = 82 + X
--> X = 18

Required ratio = (18 - 10) : (18 - 6) = 8 : 12 = 2 : 3

IMO Option C
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Re: In a survey among students, it was found that 48% preferred coffee, 54   [#permalink] 03 Nov 2019, 03:28
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In a survey among students, it was found that 48% preferred coffee, 54

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