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# ratio problem

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Manager
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ratio problem [#permalink]  25 May 2010, 07:51
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I know this will be a easy question for a lot of you.. but i really didnt understand the solution.. can someone help

The ratio, by weight, of coffee to mate to water in a certain cup of coffee is 6:2:15. The coffee is
altered so that the ratio of coffee to mate is halved while the ratio of coffee to water is doubled. If
the altered coffee will contain 16 grams of mate, how many grams of water does it contain after
alteration?
13
(A) 12
(B) 15
(C) 30
(D) 60
(E) 100
Solution
The current ratio of coffee to mate is 6:2, when halved, the ratio becomes 3:2 or 6:4 or 12:8. The
current ratio of coffee to water is 6:15, when doubled, the ratio is 12:15. The ratio of cofee to mate
to water, when combined, becomes 12:8:15. Based on the ratio 12:8:15, the total grams t was
divided as follows:
t
38
10
was coffee, t
38
8
was mate, and t
38
15
was water. Since t
38
8
= 16, t = (16) 76
8
38 =
and then 76 30
38
15
38
15 t = × = . So the correct answer choice is C.
Senior Manager
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Re: ratio problem [#permalink]  25 May 2010, 08:07
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Here is my take on this

c:m:w = 6:2:15

new c:m = 1/2(6/2) = 3:2

new c:w = 2(6:15) = 12:15 = 4:5

so new m:c:w = 2:3
4:5
= 8:12:15 ( notice how i combined the two ratios by multiplication by 3 and 4 of respective ratios)

m = 16 g
Let T = total amount of c + m + w then
8 / (8+12+15)T = 16 x 35/8 = 70g

then w = 15/35 x 70 = 30g

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Re: ratio problem [#permalink]  12 Sep 2011, 08:53
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C:M:W=6:2:15
C:M is halved so C:M=3:2
C:W is doubled = 12:15
Now M:C =2:3 and C:W=12:15
M:C=8:12 C:W=12:15
M:C:W=8:12:15
New mix contains 16gms of Mate
8x=16
x=2
Water will be 15x=15*2=30gms
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Re: ratio problem [#permalink]  12 Sep 2011, 12:28
c:m:w = 6:2:15

c:m (halved) = 6:4 .... we can write is as 12:8
c:w (doubled) = 12:15

c:m:w = 12:8:15
if mate is 16g, then water must be 30g(15*2)
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Re: ratio problem [#permalink]  12 Sep 2011, 14:23
Yeah, I thought about halving the coffee at the start as well, but decided against it, because otherwise you would have to perform 2 operations on the water

Instead, you double the mate and then halve the water.

The result would taste horrible, but would give you answer C.
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Re: ratio problem   [#permalink] 12 Sep 2011, 14:23
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