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 6 of 10.
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.
Garima said:
1 decade ago
It is possible that drawn out 8l wine from the mixture the answer can be 24l, because whenever the wine is drawn from the liquid it is again filled with the water in the same amount.
Rahul said:
1 decade ago
Is another easy method for this problem?
MaraM said:
1 decade ago
Hello anybody explain of to me.
81 is how its coming?
81 is how its coming?
Manju said:
1 decade ago
Not understood. Can anyone help? Why divide by x? Also shouldn't ratio be directly used as a fraction?
Sibi said:
1 decade ago
I don't understand this problem. Please explain me clearly.
Rupesh said:
1 decade ago
Answer for x.
As the ratio is 16/65 (Wine:Water).
So the amount wine/total mixture = 16/65+16 = 16/81.
Here x = 81.
As the ratio is 16/65 (Wine:Water).
So the amount wine/total mixture = 16/65+16 = 16/81.
Here x = 81.
Pallavi Jha said:
1 decade ago
Can anyone explain why it is divided by x?
Nishad raut said:
1 decade ago
65 is given and 16 is assumed..so ans is assumed..
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PUNITH MISHRA P said:
1 decade ago
It is like this:
x(1-(8/x)^4)-(1) gives quantity of wine, whereas final ratio is 16/81. So final wine quantity is (16/81)*x which is equal to (1).
x(1-(8/x)^4)-(1) gives quantity of wine, whereas final ratio is 16/81. So final wine quantity is (16/81)*x which is equal to (1).
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