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 9 of 10.
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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Sanjay said:
1 decade ago
Could anyone explain the method above?
I couldn't make out why x is divided when it should have been divided by the quantity of water.
I couldn't make out why x is divided when it should have been divided by the quantity of water.
Pandit said:
1 decade ago
Lets,
The volume of the drum is x.
In 1st operation 8 liter is drawn.
Remaining pure wine is x-8.
Now. If we draw whole volume = the volume of wine is drawn is x-8.
""""""""""''' 1 unit volume="""""""""""""""""""""""""" (x-8) /x.
""""""""""'''8 unit volume=""""""""""""""""""""""""""8*(x-8) /x.
The volume of wine remaining after 1st operation is (x-8) -{8* (x-8) /x} = { (x-8) ^2}/x...
Similarly in 4th draw pure wine is x (1-8/x) ^4.
The volume of the drum is x.
In 1st operation 8 liter is drawn.
Remaining pure wine is x-8.
Now. If we draw whole volume = the volume of wine is drawn is x-8.
""""""""""''' 1 unit volume="""""""""""""""""""""""""" (x-8) /x.
""""""""""'''8 unit volume=""""""""""""""""""""""""""8*(x-8) /x.
The volume of wine remaining after 1st operation is (x-8) -{8* (x-8) /x} = { (x-8) ^2}/x...
Similarly in 4th draw pure wine is x (1-8/x) ^4.
Murali said:
1 decade ago
After n operations the wine left is {(x-8)^n}/x^n-1.
However, at the end of every cycle the total quantity is x. Therefore quantity of water left after n operations is x-quantity of wine left= x-{(x-8)^n}/x^n-1.
Now, dividing quantity of wine left by quantity of water left we get: {(x-8)^n}/{x^n-(x-8)^n} = 16/65. Substitute each one of the options n see which one matches rather than going to solve this complex expression.
However, at the end of every cycle the total quantity is x. Therefore quantity of water left after n operations is x-quantity of wine left= x-{(x-8)^n}/x^n-1.
Now, dividing quantity of wine left by quantity of water left we get: {(x-8)^n}/{x^n-(x-8)^n} = 16/65. Substitute each one of the options n see which one matches rather than going to solve this complex expression.
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.
PRAVU said:
1 decade ago
@Sanjay.
Pure wine is divided by total amount in the vessel, i.e. x.
So, pure wine: water = 16:65 OR it can be said as pure wine:total = 16:(16+65) = 16:81
Note that in each operation the total is always x litre.
Pure wine is divided by total amount in the vessel, i.e. x.
So, pure wine: water = 16:65 OR it can be said as pure wine:total = 16:(16+65) = 16:81
Note that in each operation the total is always x litre.
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