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 3 of 10.
Santosh said:
5 years ago
Let x be initial volume(in lit) of wine.
By formula final amount of wine after n(=4) iteration = x{1 - 8/x}^4 ---->1.
Given the final ratio of wine to water is 16:65.
So the volume of wine in the final iteration is {16/(16+65)}x -------> 2.
Equate 1 and 2,
And we get x=24.
By formula final amount of wine after n(=4) iteration = x{1 - 8/x}^4 ---->1.
Given the final ratio of wine to water is 16:65.
So the volume of wine in the final iteration is {16/(16+65)}x -------> 2.
Equate 1 and 2,
And we get x=24.
Reeya said:
1 decade ago
I think the question is wrong. I know it can never be said as an excuse, but if the the ratio of wine remaining to that of water is 16:65, then we can take the denominator, wine originally as x.
i.e., (x (1-8/x) ^4) / (x) = 16/ (16+65) = 16/81.
Correct me if I am wrong.
i.e., (x (1-8/x) ^4) / (x) = 16/ (16+65) = 16/81.
Correct me if I am wrong.
Nitin said:
10 years ago
Let wine left be x,
4 times 8 liter wine removed = 4*8 = 32.
Therefore wine left = (x-32).
Water filled 4 times = (4*8) = 32.
Therefore ratio of (Quantity of wine left/Quantity of water).
= (16/65).
Therefore ( (x-32)/32) = (16/65).
On solving we get x = 39.87~40.
4 times 8 liter wine removed = 4*8 = 32.
Therefore wine left = (x-32).
Water filled 4 times = (4*8) = 32.
Therefore ratio of (Quantity of wine left/Quantity of water).
= (16/65).
Therefore ( (x-32)/32) = (16/65).
On solving we get x = 39.87~40.
Chatrapathi said:
1 decade ago
Let "x" liters of wine was present.
This wine was replaced by 8 liters of water for 4 times. So, wine at present is x[1-(8/x)]^4.
Also given that wine to water ratio at present is 16:65. So wine at present = 16 x/16+65.
So x[1-(8/x)]^4 = 16 x/16+65.
x = 24.
This wine was replaced by 8 liters of water for 4 times. So, wine at present is x[1-(8/x)]^4.
Also given that wine to water ratio at present is 16:65. So wine at present = 16 x/16+65.
So x[1-(8/x)]^4 = 16 x/16+65.
x = 24.
Sahil said:
1 decade ago
Since each time we are adding 8 litres of water and talking away 8 litres. So total composition is same only the proportions of individual componnts will change.
So talking water as x litre is wrong.
He has calculated the ratio of wine to whole soln. !
So talking water as x litre is wrong.
He has calculated the ratio of wine to whole soln. !
Bappa said:
1 decade ago
Lets wine x
after 1st time wine remain x-8
now ratio of wine:water x-8:8
so 2nd time wine removed=(x-8)*(8/x)
after 2nd time wine remain=(x-8)-(x-8)*(8/x)
=(x-8){1-8/x}
=x(1-8/x)(1-8/x)
=x(1-8/x)^2
.........
for n time removaline remain=x(1-8/x)^n.
after 1st time wine remain x-8
now ratio of wine:water x-8:8
so 2nd time wine removed=(x-8)*(8/x)
after 2nd time wine remain=(x-8)-(x-8)*(8/x)
=(x-8){1-8/x}
=x(1-8/x)(1-8/x)
=x(1-8/x)^2
.........
for n time removaline remain=x(1-8/x)^n.
Rattle said:
1 decade ago
@Prajakt
the soln. assumes in the 1st line that the original quantity of wine be x. the question says the wine removed is replaced with water(obviously, in equal amount). Since we assume x as wine quantity, this replaced water quantity is also x.
the soln. assumes in the 1st line that the original quantity of wine be x. the question says the wine removed is replaced with water(obviously, in equal amount). Since we assume x as wine quantity, this replaced water quantity is also x.
Barath s said:
4 years ago
For those who don't understand why it is divided by x?
Here in 16/81, 81 can be taken as total mixture are 81y is the total capacity of the cask. So x is the total wine that was kept at first which is nothing but the total capacity of the cask.
Here in 16/81, 81 can be taken as total mixture are 81y is the total capacity of the cask. So x is the total wine that was kept at first which is nothing but the total capacity of the cask.
(2)
Amit said:
1 decade ago
After the first step of adding 8 liters of water, the cask contains a mix of wine and water so the next time we take 8 liters out, it could have 75 % wine or 35 % wine or any other amount. So, how can we calculate the final proportion of wine?
Amit said:
8 years ago
As 65:15 is wine as to water ratio is given means total solution was (65+16)=81 which was totally quantity of wine before removal of 8 liter wine that's why it is x = total =81.
Where x=initial quantity of wine.
W:T = x(1-(8/x))^4:x = 16/81.
Where x=initial quantity of wine.
W:T = x(1-(8/x))^4:x = 16/81.
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