The question below is one of the toughest I have seen.
Total bags are 453. Each bag contains at least one of the following: raisin, almonds and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is 1/5 the number of bags that contain only almonds. 210 bags contain almonds. How many bags cotain only one kind of item
Ans is 320.
This is how I have solved.
bags only Raisins= 10 times bags contain only peanuts.
bags only Almonds= 20 times the bags that contain raisins and peanuts.
bags that contain only peanuts=1/5 the number of bags that contain only almonds.
r=10p
r+P=y name Y
A=20(r+P) or same as (20Y)
p=1/5 A or 1/5 (20Y) or 4y
so P =4y
A =20Y
R=10p or 40Y
so 64Y What Then.
How do you get 320.
Thanks
Khurram
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Ian Stewart
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What may make it tough is that there's a problem with the question:khurram wrote:The question below is one of the toughest I have seen.
Total bags are 453. Each bag contains at least one of the following: raisin, almonds and peanuts. The number of bags that contain only raisins is 10 times the number of bags that contain only peanuts. The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts. The number of bags that contain only peanuts is 1/5 the number of bags that contain only almonds. 210 bags contain almonds. How many bags cotain only one kind of item
Ans is 320.
- 210 bags contain almonds.
The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts.
Ignoring that, you know that 210 bags contain almonds. Thus, the other kinds of bags add to 453-210 = 243. These are the bags containing Peanuts only (P), Raisins only (R), and Peanuts+Raisins (PR).
-From the statement I quoted above, we ought to be able to calculate PR (it's 210/20 = 10.5, which doesn't make any sense, but that's what the questions says!).
-We're also told that R = 10P
-Thus, P + 10P + 10.5 = 243.
-From that, you can find P.
-The number of 'almonds only' bags is 5P, from the info in the question. The question asks us, finally, to find P + R + A = P + 10P + 5P, so with P we can find the answer.
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netigen
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Are you sure you typed the question right:
The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts = 210
number of bags that contain only raisins and peanuts = 210/20 != an integer?
The number of bags that contain almonds is 20 times the number of bags that contain only raisins and peanuts = 210
number of bags that contain only raisins and peanuts = 210/20 != an integer?
i think the question says the bag that contains ONLY almondsis 20 times the number of bags that contains only raisins and peanuts,
so we have to keep in mind that the bags that contains almonds and the bag that contains only almonds are two different things!
so we have to keep in mind that the bags that contains almonds and the bag that contains only almonds are two different things!
