In a certain flower shop, which stocks four types of

Question

In a certain flower shop, which stocks four types of flowers, there are 1/3 as many violets as carnations, and 1/2 as many tulips as violets. If there are equal numbers of roses and tulips, what percent of the flowers in the shop are carnations?

a) 10%
b) 33%
c) 40%
d) 50%
e) 60%

arsaboo · Answer

1/3 as many violets as carnations could be written as

v = c/3 
similarly we can write 
t = v/2
i.e. t =c/6
therefore, r = c/6

We can write r+t+c+v = 100%
therefore c/6 + c/6 + c + c/3 =100
10c/6 = 100

Threfore c = 60%

sudhagar · Answer

OA is E.

 

I wasted sometime in assuming that carnation = 1/3violets. Fortunately there was no answer that matched my answer. So I corrected the equation and tried again. 

Princeton review quotes this as a tough word question.

FN · Answer

how is it D 50%?

say C=6

then 1/3 of C=2 =violets

then 1/2 of Violets is 1=Roses=tulips..

total=10 flowers 6 are Carnation

sudhagar · Answer

Something terribly wrong with me. Since yesterday I have made 4 careless errors in the post. 

I have edited the post and the correct answer is E (60%)

TeHCM · Answer

"there are as many.....as...." are kind of tricky. 

V=1/3C, C=3V
T=1/2V, V=2T
R=T=1/2V

Question asks: C/(V+C+T+R)

So 3V/(V+3V+1/2V+1/2V) = 3V/5V = 60%

E

remgeo · Answer

Since the answer contains percentages, the easiest way is to take the total no of flowers as an arbitrary no. 
Let us take total no of flowers = 12. 
R + V + C + T = 12 

R + 1/3C + C + T = 12

R + 1/3C + C + 1/6C = 12

1/6C + 1/3C + C + 1/6C = 12

C = 36/5

Now percentage of C = C/Total * 100
ie. (36/5*12 ) * 100 = 60%

Answer = 60%

mophead · Answer

Can you do this in terms of V instead of C? i.e. changing them all to units of V and then doing the division?

Thanks.

sudhagar · Answer

Since the question has asked to get the % of carnations, it would save time if we do in terms of C. We could do it in terms of V as well, but there would be an additional step at the end.

In a certain flower shop, which stocks four types of

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