Three vessels A, B and C of capacity 120 litres each contain a mixture

Question

Three vessels A, B and C of capacity 120 litres each contain a mixture of alcohol and spirit. Vessel A contains 100 litres of the mixture with 65% alcohol. Vessel B has 70% alcohol and this vessel is half empty. The vessel C has 80 litres of mixture out of which 20 litres are spirit. Now, the mixture from vessel A is poured into vessel B until vessel B is completely filled. Then the mixture from vessel B is poured into vessel until C is completely filled. Now the entire mixture from vessel C is poured into the vessels A and B. What is the ratio of alcohol in vessels A and B ?

A. 4/5
B. 9/10
C. 84/83
D. 28/27
E. 23/22

Are You Up For the Challenge: 700 Level Questions

A. 4/5
B. 9/10
C. 84/83
D. 28/27
E. 23/22

Are You Up For the Challenge: 700 Level Questions

sevenfive · Accepted Answer

Alcohol and Spirit are in this quantity 
A - 65 | 35 
B - 42 | 18
C - 60 | 20

Total Alcohol - 167
Only Option C has ratios which divides 167 
So Option C

ThatDudeKnows · Answer

Starting case:
A has 100 total: 65 alcohol, 35 spirit.
B has 60 total: 42 alcohol, 18 spirit.
C has 80 total: 60 alcohol, 20 spirit.

We pour 60 from A to B. Of that 60, 65% (or 39) is alcohol and 21 is spirit. 
A now has 40 total: 26 alcohol and 14 spirit. 
B now has 120 total: 81 alcohol, 39 spirit.

We pour 40 from B to C. Of that 40, 81/120 is alcohol, so 81/3=27 is alcohol and 13 is spirit. 
B now has 80 total: 54 alcohol and 26 spirit.
C now has 120 total: 87 alcohol and 33 spirit.

We pour 80 from C into A and 40 from C into B, so A gets 2/3rds (58 alcohol and 22 spirit) and B gets 1/3 (29 alcohol and 11 spirit).
A now has 84 alcohol and 36 spirit. 
B now has 83 alcohol and 37 spirit.

Alcohol in A : alcohol in B
84:83

Answer choice C.

abhinavchitre13 · Answer

Great question !!!

Posted from my mobile device

samarpan.g28 · Answer

I calculated all the way, it took me 10 minutes to get (C) as the answer,  Bunuel  please help with a time-saving approach.

Kinshook · Answer

Three vessels A, B and C of capacity 120 litres each contain a mixture of alcohol and spirit. Vessel A contains 100 litres of the mixture with 65% alcohol. Vessel B has 70% alcohol and this vessel is half empty. The vessel C has 80 litres of mixture out of which 20 litres are spirit. Now, the mixture from vessel A is poured into vessel B until vessel B is completely filled. Then the mixture from vessel B is poured into vessel until C is completely filled. Now the entire mixture from vessel C is poured into the vessels A and B. What is the ratio of alcohol in vessels A and B ?

A. 4/5
B. 9/10
C. 84/83
D. 28/27
E. 23/22

Are You Up For the Challenge: 700 Level Questions

What is the ratio of alcohol in vessels A and B ?

Vessel A:
Total = 100 litres
Alcohol = 65%*100 =65 litres

Vessel B:
Total = 50%*120 = 60 litres
Alcohol = 70%*60 = 42litres

Vessel C:
Total = 80 litres
Alcohol = 80-20 = 60 litres 
% alcohol = 60/80 =0.75 = 75%

Now, the mixture from vessel A is poured into vessel B until vessel B is completely filled.

Vessel A:
Total = 100-60 =40 litres 
Alcohol = 65% of 40 L= 26 litres

Vessel B:
Total = 60+60= 120 litres
Alcohol = 42 + (65-26) = 81 litres 
Alcohol % = 81/120=0.675 = 67.5%

Then the mixture from vessel B is poured into vessel until C is completely filled.

40 litres of vessel B is poured in vessel C

Vessel B:
Total = 120-40= 80 litres
Alcohol = 81/120*80=54 litres

Vessel C:
Total = 80+40=120 litres
Alcohol = 60 + (81-54) = 87 litres 
% alcohol = 87/120=0.725 = 72.5%

Now the entire mixture from vessel C is poured into the vessels A and B.

Vessel A:
Total = 40+ 80= 120litres 
Alcohol = 26+ 87/120*80 =84 litres

Vessel B:
Total = 80+40=120 litres
Alcohol = 54+87/120*40=83 litres

the ratio of alcohol in vessels A and B = 84/83

IMO C

onlyPlanA · Answer

Took me full 10 mins to solve this.

Given that, 
100 lt mixture in Vessel A = 65% Alcohol = 65 lt alcohol
60 lt mixture in Vessel B = 70% Alcohol = 42 lt alcohol
80 lt mixture in Vessel C = 75% Alcohol = 60 lt alcohol

When the mixture is transferred from A to B, B becomes full. Hence, 60 lt of mixture is taken from A.
So, alcohol content in B = (65/100) * 60 + 42 = 81 lt
New percentage of alcohol in B = 81/120 * 100 = 67.5%

40 lt of this mixture is now transferred to Vessel C.
Thus, alcohol content in C = 67.5% * 40 + 60 = 87 lt
New percentage of alcohol in C = 87/120 * 100 = 72.5%

Now the entire contents of C is transferred back to A and B
Since, 40 lt mixture was left in A, 80 lt of mixture from C will be taken.
Hence, new alcohol content in A = 65/100 * 40 + 135/200 * 80 = 84 lt ------- (Remember new percentage of alcohol in B is 135/2%)

And, 80lt of mixture was left in B, so the remaining 40lt mixture in Vessel C will be taken.
Hence, new alcohol content in B = 135/200 * 80 + 145/200 * 40 = 83

Hence, the ratio of alcohol contents in A and B = 84/83.

Pheewwww... 😓

Three vessels A, B and C of capacity 120 litres each contain a mixture

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GMAT Problem Solving (PS) Questions

Three vessels A, B and C of capacity 120 litres each contain a mixture

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

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Perfect 805 Score Debrief by Julia

My Rewards