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Math Expert V
Joined: 02 Sep 2009
Posts: 64951
1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to  [#permalink]

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Difficulty:   55% (hard)

Question Stats: 68% (02:56) correct 32% (03:08) wrong based on 66 sessions

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1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to water 5:1, 3:2 and 4:3, respectively are mixed. What would be the ratio of milk and water in the resulting mixture?

A. 787:1260
B. 747:473
C. 787:473
D. 747:443
E. 787:443

Are You Up For the Challenge: 700 Level Questions

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GMAT Club Legend  V
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Joined: 08 Jul 2010
Posts: 4313
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1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to  [#permalink]

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Bunuel wrote:
1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to water 5:1, 3:2 and 4:3, respectively are mixed. What would be the ratio of milk and water in the resulting mixture?

A. 787:1260
B. 747:473
C. 787:473
D. 747:443
E. 787:443

Are You Up For the Challenge: 700 Level Questions

Total Milk = (5/6)*1 + (3/5)*2 + (4/7)*3 = (5/6)+(6/5)+(12/7) = (175+252+360)/210 = 787/210

Total Quantity of Mixture = 1+2+3 = 6 Lt.

i.e. Water = 6 - (787/210) = 473/210

Milk / Water = 787/473

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Re: 1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to  [#permalink]

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Bunuel wrote:
1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to water 5:1, 3:2 and 4:3, respectively are mixed. What would be the ratio of milk and water in the resulting mixture?

A. 787:1260
B. 747:473
C. 787:473
D. 747:443
E. 787:443

first and second mixtures of water:
1/6--1--m--2--2/5
1/2=2/5-m/m-1/6
m=29/90 or 29 parts water over total

first+second and third mixtures of water:
29/90--1--n--1--3/7
1/1=3/7-n/n-29/90
n=473/1260 or 473 parts of water over total

final mixture milk to water:
1260-473:473=787:473

Ans (C)
Math Expert V
Joined: 02 Aug 2009
Posts: 8753
Re: 1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to  [#permalink]

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1
Bunuel wrote:
1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to water 5:1, 3:2 and 4:3, respectively are mixed. What would be the ratio of milk and water in the resulting mixture?

A. 787:1260
B. 747:473
C. 787:473
D. 747:443
E. 787:443

Are You Up For the Challenge: 700 Level Questions

To ease the calculations, let us get all ratios in terms of equal total quantity..
We have ratios with quantities 5x+x=6x, 3y+2y=5y and 4z+3z=7z...

LCM of 6,5,7 is 6*5*7=210...
SO M:W= 5:1=5*7*5:5*7=175:35..........1 l means 175 and 35 of M and W
3:2=3*6*7:2*6*7=126:84.......2 l means 126*2 and 84*2 of M and W
4:3=4*6*5:3*6*5=120:90....3l means 120*3 and 90*3 of M and W.

Total M = 175+126*2+120*3=175+252+360=787
Total W=35+84*2+90*3=35+168+270=473

Ratio M:W = 787:473

C
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Re: 1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to  [#permalink]

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2
Can we solve it by this approach?
5:1=5+1=6 ,
3:2=3+2=5
4:3=4+3=7
LCM of 6*5*7=210

A) 787:1260 = 787+1260 = 2047/210 = (non integer)
B) 747:473 = 747+473 = 1220/210 = (non integer)
C) 787:473 = 787+473 = 1260/210 = (integer)
D) 747:443 = 747+443 = 1190/210 = (non integer)
E) 787:443 = 787+443 = 1230/210 = (non integer)
Hence C.

Posted from my mobile device Re: 1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to   [#permalink] 06 Jun 2020, 08:46

# 1l, 2l, and 3l, mixtures of milk and water, with the ratios of milk to  