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.
Venkat said:
6 years ago
@All.
16x/81 is the quantity of wine in the mixture is given so equate to x(1-8/x)^4. (x is fixed litres of mixture).
16x/81 is the quantity of wine in the mixture is given so equate to x(1-8/x)^4. (x is fixed litres of mixture).
Moideen said:
7 years ago
Well explained, Thanks @ Jayaraj @Jyoti.
Jyoti said:
7 years ago
@Naeem and @Shamika,
Here 81 is the amount of total mixture (16+65=81). It is the ratio of wine to total mixture. Here, the water was being replaced each time, so the total quantity of the mixture is still 'x' which is 81.
Here 81 is the amount of total mixture (16+65=81). It is the ratio of wine to total mixture. Here, the water was being replaced each time, so the total quantity of the mixture is still 'x' which is 81.
Naeem said:
7 years ago
How come 81 in the denominator?
Shamika said:
7 years ago
How come 81?
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)
Purushuttam said:
7 years ago
Have there any explanation of these laws [x(1-y/x)*n] where y<x?
Prakash said:
7 years ago
Use the formula (x-8/x)n = 16 / 81.
where n is 4,
x is original liquid (x-8) is the original liquid remaining after the exchange that is 16,
x the original quantity will be 65+16=81.
where n is 4,
x is original liquid (x-8) is the original liquid remaining after the exchange that is 16,
x the original quantity will be 65+16=81.
Jayaraj said:
8 years ago
16:65 is wine to water ratio.
That means if there is at total of 81 parts of solution 16 part will be wine and 65 part will be water (81=16+65).
So wine to total solution amount ration would be 16:81.
total solution amount =x.
That means if there is at total of 81 parts of solution 16 part will be wine and 65 part will be water (81=16+65).
So wine to total solution amount ration would be 16:81.
total solution amount =x.
Aniket said:
8 years ago
What if instead of wine it would have been 6 litres of solution of wine and water for second time?
(1)
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