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Tricky one!

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by Ozlemg » Thu Jun 02, 2011 8:59 am
24 lbs of coffee P and 25 lbs of coffee V are mixed to make coffee X and Y. The ratio of P to V in coffee X is 4 to 1, in Y is 1 to 5. How much of P is contained in the mixture X?

A. 10
B. 20
C. 30
D. 40
D. 45
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Source: — Problem Solving |

by cans » Thu Jun 02, 2011 9:07 am
let p of P in X and thus 24-p in Y
similarly let v of V in X and thus 25-v in Y
p/v=4/1 => p=4v => v=p/4
(24-p)/(25-v)=1/5
(24-p)/(25-(p/4)) = 1/5
5(24-p) = (100-p)/4
380 = 19p
p=20
IMO B
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by Frankenstein » Thu Jun 02, 2011 9:07 am
Hi,
Mixture----P---V
X---------4x---x
Y----------y--5y
So, P =4x+y=24 and V=x+5y=25.
Solving, we get x=5 and y=4
X has 4x=20lbs of P

Hence, B
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by Ozlemg » Thu Jun 02, 2011 9:12 am
Good job guys! I am impressed.
OA B
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by GMATGuruNY » Thu Jun 02, 2011 2:36 pm
Ozlemg wrote:24 lbs of coffee P and 25 lbs of coffee V are mixed to make coffee X and Y. The ratio of P to V in coffee X is 4 to 1, in Y is 1 to 5. How much of P is contained in the mixture X?

A. 10
B. 20
C. 30
D. 40
D. 45
We can plug in the answers, which represent the amount of P in mixture X.
Since there are only 24 pounds of P in total, the correct answer cannot exceed 24.
Eliminate C, D and E.

Since in X the ratio of P:V = 4:1, the correct answer likely is a multiple of 4.
The only viable answer choice is B.

Answer choice B: 20 pounds of P in mixture in X
Since 4:1 = 20:5, there are 5 pounds of V in mixture X.
Remaining P = 24-20 = 4 pounds.
Remaining V = 25-5 = 20 pounds.
4:20 = 1:5, the correct ratio for mixture Y.

The correct answer is B.
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