A cistern contains 50 liters of water. 5 litre of water is taken out of it and replaced by wine. The process is repeated again. Find the proportion of wine and water in the resulting mixture.
A) 1:4
B) 41:50
C) 19:81
D) 81:19
E) 1:7
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the answer is A. 1:4
Ans: D
1. Water: 50 lt Wine: 0 lts
2. Taking out 5 lt of water and filling 5 lt of wine: Water: 45 lts and Wine 5 lts;
3. Taking out 5 lts of mixture and mixing the 5 lt of wine. In taking out the 5lts of mixture 45 * (5/50) lts of water and 5 * (5/50) of wine goes out and the resultant mizxture is Water 45 – 4.5=40.5 and Wine 5-0.5 = 4.5. After mixing 5 lts of wine, the size of the wine becomes 9.5. The proportion is 40.5 : 9.5 or 81:19
Sorry the anser should be 19:81
Great explanation Venki!
the question is confusing in the sense that there are two meanings of the sentence “The process is repeated again”
Meaning 1:
5 litre of water is taken out of it (again) and replaced by wine.
In that case answer should be A) 1:4
Meaning 2:
5 litre of mixture is taken out of it and replaced by wine.
In that case answer should be C) 19:81
We are sure that wine will mixup with water hence meaning 2 seems ok. But I think the answer may change if we add something which
does not mix with water.
Dear Vikas,
The process is repeated again. Explicitly saying that we are taking our 5 litre from mixture not from somewhere else.
Thanks for your new thought………..
c) 19:81…the ratio asked is that of wine to water
I have a doubt here can anyone help me to clarify:
Water: Wine =50:0 (Initially) ,then 5 litres are removed & then the water : wine ratio stands as 45:5 .It says repeat the process which means we remain 5 litres of mixture.i.e: 0.5 lts of wine & 4.5 lts of water. So at this stage water: wine =41.5:4.5 and thereafter we add 5 lts of wine thus water: wine =41.5:9.5
Wine : Water =9.5/41.5 =95/415=19/83
So as per my calculation answer has to be 19/83 .
Why am i getting diffirent answer than as per above
Looking forward to clarification
Thanks
here is your mistake
88888888888888888888888888888888888888888888
So at this stage water: wine =41.5:4.5 and thereafter we add 5 lts of wine thus water: wine =41.5:9.5
88888888888888888888888888888888888888888888
Currect,
So at this stage water: wine =40.5:4.5 and thereafter we add 5 lts of wine thus water: wine =40.5:9.5
88888888888888888888888888888888888888888888
Wine : Water =9.5/40.5 =95/405=19/81
So as per my calculation answer has to be 19/81 .
Why am i getting diffirent answer than as per above
Looking forward to clarification
Thanks
c
(C) is correct. If 5 L of water are removed and replaced with 5 L of wine and the resulting mixture is mixed thoroughly, 1/10 (=5/50) of the resulting mixture is wine and 9/10 (=45/50) is water. If 5 L of this new mixture are then removed and replaced with 5 L of wine, there are 19/2 L (5 L – 0.5 L + 0.5 L) of wine and 81/2 L (45 L – 9/2 L) of water at the end of the day. The ratio of wine to water is then 19:81.