Two vessels having volumes in the ratio 3:5 are filled with

Question

Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:170

Bunuel · Accepted Answer

Vessel A = 300 gallons --> milk = 120, water = 180;
Vessel B = 500 gallons --> milk = 375, water = 125;

Vessel A + B = 800 gallons --> milk = 495, water 305.

The ratio = 495/305 --> reduce by 5 = 99/61.

Answer: A.

StormedBrain · Answer

let volume of first vessel is 3 and second vessel is 5.

total volume of milk = 3(2/5)+5(3/4) = 99/20
total volume of water= 3(3/5)+5(1/4) = 61/20

Milk : water = 99:61

Predecessor · Answer

I solved this by drawing two canisters with the milk/water proportions and then set them equal (2:3 becomes 6:9 and 3:1 becomes 6:2). Once we draw the final (biggest) canister we can see that the proportion of milk (6+6=12) is larger than the proportion of water (2+9=11) and the answer "A"is the only one that gives us this choice

grant1377 · Answer

Can you explain how you quickly arrived at 300 : 500 gallons?

I understand that A needs to be a multiple of 5, and B of 4, but I'm not quite sure how to find good values to use in a time efficient manner. I started at 15 and 25, then went up, and it took me too long...

Thanks

Bunuel · Answer

I chose big numbers in the ratio 3 to 5. So, that A is also a multiple of 5 and B is also a multiple of 4 (since the ratio of milk and water in the two vessels are 2:3 (5 parts) and 3:1 (4 parts) respectively, then A should be a multiple of 5 and B should be a multiple of 4).

KarishmaB · Answer

A few pointers when assuming numbers:
Try to stick to multiples of 10 or 100 as the case may be. 
Given 3:5, I would first look at 30 and 50 or 300 and 500. I would not look at 15 and 25 because when I am assuming value, nothing says they need to be as small as possible. Answer won't change even if they are a little larger but with multiples of 10, my calculations may be much simpler.
Next, I need first one to be a multiple of 5 and the next one to be a multiple of 4. 30 and 50 will not satisfy but 300 and 500 will.

sayansarkar · Answer

@karishma:

I think we can always multiply the two total parts of the proportions, i.e 2:3 =5 parts and 3:1 = 4 parts and 5*4=20

then follow the process that bunuel explained. 
???

KarishmaB · Answer

I am not sure what you mean. Do you mean to say that we can take the volume of vessel A as 20 gallons? or do you mean that we can take the volume of vessel A as 20*3 gallons?

Note that either case will be correct because when you are assuming numbers, you will get the correct answer for every correct set of numbers you take. The point is of convenience.
If vessel A has volume of 20 gallons, the volume of vessel B will not be a whole number.

Vessel A = 20 gallons --> milk = 8, water = 12;
Vessel B = 100/3 gallons --- complications

If volume of vessel A is taken as 20*3 = 60 gallons, then it is fine.
Vessel A = 20*3 gallons = 60 gallons --> milk = 24, water = 36;
Vessel B = 20*5 gallons = 100 gallons --> milk = 75, water = 25;

Total milk:water = (24+75):(36+25) = 99:61

mumbijoh · Answer

Dear Karishma,
Please help explain how we can use your scale method to solve this question.
Here'e up to where i got.

2/5 3/8 ¾
 31/40 9/8

Then I flipped the two ratios so its 9/8 to 31/40
Then I got stuck.

Ps. Sorry the lines wouldn't appear

KarishmaB · Answer

According to scale method:

w1/w2 = (C2 - Cavg)/(Cavg - C1)

3/5 = (3/4 - Cavg)/(Cavg - 2/5) (Working with only milk here. Note that concentration of milk is 3/4 in second vessel since milk:water is 3:1. Also, the ratio of the volume of two solutions that are mixed is 3:5. It is not the concentration of milk in the final solution. So w1/w2 = 3/5)

8/5Cavg = 3/4 + 6/25 
Cavg = 99/160

Milk:Water in final solution = 99:61

mumbijoh · Answer

Karishma,
Your totally right.I must have misread that question.Thanks a lot for the clarification!

gracie · Answer

let x=ratio of milk to total volume
3(2/5)+5(3/4)=8x→
x=99/160
160-99=61
ratio of milk to water=99:61
A

AkshdeepS · Answer

I was not able to decipher the way to solve this.

I knew by looking at the ratios that milk is more than water, and only option A shows more milk than water.

In rest of the choices water is more than milk as per given ratios.

Bunuel  : Is my logic right?

Anton1234 · Answer

Neat way of finding easy ratios to divide quickly

You want 3:5 to easily flow into 2:3 and 3:1

In essence the 3 in initial ratios needs to divide by 5 and the 5 in initial ratio needs to divide by 4.

Find LCM which is 4*5 = 20

Now you can rearrange initial ratio by multiplying both by 20 --> you get 60:100

Now you can easily find the ratio of milk and water in the vessels themselves

for 2:3 5 parts total is 60/12 --> so 2 parts is 24 and 3 parts is 36

Repeat for the second ratio

MartyMurray · Answer

Two vessels having volumes in the ratio 3:5 are filled with water and milk solutions. The ratio of milk and water in the two vessels are 2:3 and 3:1 respectively. If the contents of both the vessel are empties into a larger vessel, find the ratio of milk and water in the larger vessel.

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160

We can solve this one quickly by noticing that the ratio with the big difference, 3:1 milk to water, is in the vessel with the larger size, 5, whereas the closer ratio, 2:3 milk to water, is in the vessel with the smaller size, 3.

So, the ratio with the bigger difference in the larger vessel will predominate, meaning that, when everything is combined in the larger vessel, there will be more milk than water.

Then, checking the answer choices, we can see that there is only one in which the milk side is larger than the water side, choice (A).

A) 99:61
B) 99:160
C) 61:160
D) 61:99
E) 99:160

Correct answer:   A

luisdicampo · Answer

Deconstructing the Question  
Two vessels have volumes in ratio  3:5 . 
Vessel 1 has Milk:Water =  2:3 . 
Vessel 2 has Milk:Water =  3:1 . 
All contents are poured together. Find the final Milk:Water ratio.

Step-by-step  
Let volumes be:
 V_1=3k,\ V_2=5k

Vessel 1 (2:3 → total 5 parts):
Milk fraction =  \frac{2}{5} , Water fraction =  \frac{3}{5} 
 M_1=3k\cdot\frac{2}{5}=\frac{6k}{5} 
 W_1=3k\cdot\frac{3}{5}=\frac{9k}{5}

Vessel 2 (3:1 → total 4 parts):
Milk fraction =  \frac{3}{4} , Water fraction =  \frac{1}{4} 
 M_2=5k\cdot\frac{3}{4}=\frac{15k}{4} 
 W_2=5k\cdot\frac{1}{4}=\frac{5k}{4}

Total milk:
 \frac{6k}{5}+\frac{15k}{4}=\frac{24k}{20}+\frac{75k}{20}=\frac{99k}{20}

Total water:
 \frac{9k}{5}+\frac{5k}{4}=\frac{36k}{20}+\frac{25k}{20}=\frac{61k}{20}

So final ratio:
 M:W = 99:61

Answer: 99:61

Two vessels having volumes in the ratio 3:5 are filled with

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