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 7 of 10.
Vijay said:
9 years ago
If this process done with 5 litres only one time, and the given ratio is 361:39. What will be the answer?
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.
Dee said:
8 years 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.
After 3rd time wine remain=[x(1-8/x)^2]-[x(1-8/x)^2]x/8.
= [x(1-8/x)^2]{1-8/x}
= [x(1-8/x)^2](1-8/x)
= x(1-8/x)^3 and so on;
For n operation 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.
After 3rd time wine remain=[x(1-8/x)^2]-[x(1-8/x)^2]x/8.
= [x(1-8/x)^2]{1-8/x}
= [x(1-8/x)^2](1-8/x)
= x(1-8/x)^3 and so on;
For n operation remain=x(1-8/x)^n.
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.
Sajan said:
8 years ago
Explanation for (x(1 - 8/x)pow 4)/x =16/81.
In question it's given water/wine = 16/65,
We assumed x= total wine in cask,
That means total capacity of cask is x,
So looking at ratio 16/65 we can see that total
Capacity is (16+65) = 81.
(x(1 - 8/x)pow 4) is nothing but the wine replaced by water, In other word, it is the quantity of water in a final mixture of water and wine.
So, (x(1 - 8/x)pow 4)/x must be 16/81.
In question it's given water/wine = 16/65,
We assumed x= total wine in cask,
That means total capacity of cask is x,
So looking at ratio 16/65 we can see that total
Capacity is (16+65) = 81.
(x(1 - 8/x)pow 4) is nothing but the wine replaced by water, In other word, it is the quantity of water in a final mixture of water and wine.
So, (x(1 - 8/x)pow 4)/x must be 16/81.
Venky said:
8 years ago
It should be 16:81.
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)
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.
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.
Purushuttam said:
7 years ago
Have there any explanation of these laws [x(1-y/x)*n] where y<x?
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