Aptitude - Alligation or Mixture - Discussion
Discussion Forum : Alligation or Mixture - General Questions (Q.No. 14)
14.
8 litres are drawn from a cask full of wine and is then filled with water. This operation is performed three more times. The ratio of the quantity of wine now left in cask to that of water is 16 : 65. How much wine did the cask hold originally?
Answer: Option
Explanation:
Let the quantity of the wine in the cask originally be x litres.
| Then, quantity of wine left in cask after 4 operations = |  |
x |  |
1 - | 8 |  |
4 |  litres. |
| x |
 |
|
x(1 - (8/x))4 | |
= | 16 |
| x | 81 |
 |
|
1 - | 8 | |
4 | = | |
2 | |
4 |
| x | 3 |
| |
|
x - 8 | |
= | 2 |
| x | 3 |
3x - 24 = 2x
x = 24.
Discussion:
96 comments Page 2 of 10.
PRAVU said:
1 decade ago
Note that in each drawing, we take out 8/x part of the remaining wine and every time the total (wine +water) is x litre.
In 1st draw, pure wine is (x-8) i.e. x(1-8/x).
In 2nd draw, pure wine is (x-8)-(8/x)(x-8) i.e x(1-8/x)^2.
Similarly in 4th draw pure wine is x(1-8/x)^4.
Wine:water=16:65 or wine:total = 16:81.
(note: 16+65 = 81).
So, x(1-x)^4/x = 16/81.
In 1st draw, pure wine is (x-8) i.e. x(1-8/x).
In 2nd draw, pure wine is (x-8)-(8/x)(x-8) i.e x(1-8/x)^2.
Similarly in 4th draw pure wine is x(1-8/x)^4.
Wine:water=16:65 or wine:total = 16:81.
(note: 16+65 = 81).
So, x(1-x)^4/x = 16/81.
Rajesh said:
5 years ago
Final wine = x{1 - 8/x}^4 ----> 1.
where x is the original wine quantity.
(As from formula)
Now given final wine to water ratio i.e.
Wine: water = 16:65.
Therefore final wine (in litres) = (16÷81)*(x) where ----> 2
81 = 16 +65 represnting total volume.
X = also representing initial total volume.
Equating 1 and 2 we will get the answer.
where x is the original wine quantity.
(As from formula)
Now given final wine to water ratio i.e.
Wine: water = 16:65.
Therefore final wine (in litres) = (16÷81)*(x) where ----> 2
81 = 16 +65 represnting total volume.
X = also representing initial total volume.
Equating 1 and 2 we will get the answer.
(1)
Prateek said:
1 decade ago
I agree with Sahil.
Another method:
Amt. of wine left is given by x(1-8/x)^4.
Amt. of water left is given by x- x(1-8/x)^4.
So x(1-8/x)^4/[x-x(1-8/x)^4] = 16:81
With this method, i got answers to a couple of questions which were same as this question. But unable to get the answer to this one. I think my method is perfectly alright.
Another method:
Amt. of wine left is given by x(1-8/x)^4.
Amt. of water left is given by x- x(1-8/x)^4.
So x(1-8/x)^4/[x-x(1-8/x)^4] = 16:81
With this method, i got answers to a couple of questions which were same as this question. But unable to get the answer to this one. I think my method is perfectly alright.
Amrita said:
6 years ago
This will be more understandable by using the fomula (Q/T)=(1-R/T)^n.
Here Q=16(present quantity,from the ratio).
T=81(total quantity of solution,16+65),
R=8(replacing quantity).
n=4.
So,
(16/81)=1-8/T)^4,
We have to find the value of T In RHS,
So by taking the fourth root of 16/8 we get 2/3,
Now by solving the eq 2/3=(1-8/T).
T=24.
Here Q=16(present quantity,from the ratio).
T=81(total quantity of solution,16+65),
R=8(replacing quantity).
n=4.
So,
(16/81)=1-8/T)^4,
We have to find the value of T In RHS,
So by taking the fourth root of 16/8 we get 2/3,
Now by solving the eq 2/3=(1-8/T).
T=24.
Sobat singh said:
8 years ago
Let cask is full of wine = x lt.
After 4 operations wine left= x(1-8/x)^4.
Ratio of water to wine after operation = 16/65.
From this ratio part of wine present after op= 16/81.
Total amount of mixture is = x(as cask is full of x quantity).
Now,
x(1-8/x)^4.
---------------- = 16/81
X
From this x = 24.
After 4 operations wine left= x(1-8/x)^4.
Ratio of water to wine after operation = 16/65.
From this ratio part of wine present after op= 16/81.
Total amount of mixture is = x(as cask is full of x quantity).
Now,
x(1-8/x)^4.
---------------- = 16/81
X
From this x = 24.
Surya said:
7 years ago
Let the quantity of the wine in the cask originally be x litres. 8 litres of wine is removed from it and replaced with water. This operation is done a total 4 times. After 4 operations,
Wine : Water = 16 : 65 or Wine : Total = 16 : 81.
[(x-8)/x]4 = 16/81
(x-8)/x = 2/3
3x - 24 = 2x
x = 24
The correct option is D.
Wine : Water = 16 : 65 or Wine : Total = 16 : 81.
[(x-8)/x]4 = 16/81
(x-8)/x = 2/3
3x - 24 = 2x
x = 24
The correct option is D.
(3)
Prashanth reddy said:
6 years ago
Here cask initially contains x lit of wine.
Each time the operation is repeated the same amount of water is replaced by wine.
So, after any number of operations, the final quantity in cask is always x.
Now wine:water = 16:65.
Wine:total mixture = 16:81.
Wine left after final operation:total mixture=16:8.
Each time the operation is repeated the same amount of water is replaced by wine.
So, after any number of operations, the final quantity in cask is always x.
Now wine:water = 16:65.
Wine:total mixture = 16:81.
Wine left after final operation:total mixture=16:8.
Vinod Reddy said:
9 years ago
Hi, anyone clears my doubt.
Logically, How can you remove only wine again after mixing 8 liters of water to the wine already present in the cask?
Does anybody know the formula for calculating no of liters of wine present if the solution removed from second time onwards contain both wine and the water?
Logically, How can you remove only wine again after mixing 8 liters of water to the wine already present in the cask?
Does anybody know the formula for calculating no of liters of wine present if the solution removed from second time onwards contain both wine and the water?
Tez said:
1 decade ago
Let the quantity of the wine in the cask originally be x liters.
Then, quantity of wine left in cask after 4 operations.
=[x (1- (8/8) ) ^4].
Hence, [{x (1- (8/x) ^4) ) }/x]=16/97.
=>[ (x-8) /x]^4=16/97.
=> (x-8) /x=2/3.1 (since 97^1/4=3.1).
=>x=22.5 Liters.
Answer should be 22.5 Liters.
Then, quantity of wine left in cask after 4 operations.
=[x (1- (8/8) ) ^4].
Hence, [{x (1- (8/x) ^4) ) }/x]=16/97.
=>[ (x-8) /x]^4=16/97.
=> (x-8) /x=2/3.1 (since 97^1/4=3.1).
=>x=22.5 Liters.
Answer should be 22.5 Liters.
Rahul.. said:
10 years ago
Given ratio i.e. 16/65 is wine/water.
Hence wine/(wine+water) is 16/81.
Total quantity of wine+water will remain fixed i.e. equal to initial quantity of wine i.e. x.
Hence final ratio of wine/(wine+water) will be (wine left/initial wine).
Hence it will be x (1-8/x)^n/x equal to 16/81.
Hence wine/(wine+water) is 16/81.
Total quantity of wine+water will remain fixed i.e. equal to initial quantity of wine i.e. x.
Hence final ratio of wine/(wine+water) will be (wine left/initial wine).
Hence it will be x (1-8/x)^n/x equal to 16/81.
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