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 5 of 10.
Sibi said:
1 decade ago
I don't understand this problem. Please explain me clearly.
Manju said:
1 decade ago
Not understood. Can anyone help? Why divide by x? Also shouldn't ratio be directly used as a fraction?
MaraM said:
1 decade ago
Hello anybody explain of to me.
81 is how its coming?
81 is how its coming?
Rahul said:
1 decade ago
Is another easy method for this problem?
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.
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.
UlTiMaTe said:
10 years ago
If you guys really do this maths then see this technique other than wrong methods.
The question is - "How much wine did the cask hold originally?".
So the method is :
(liquid A left after n'th operation) / (liquid B left after n'th operation) =[ (1- (b/a))^n]/[1- (1- (b/a) ^n].
Here, a= total amount of vessel(a.k.a wine);
b = amount of other liquid poured(a.k.a. water);
n = no of operations had done.
In this question they also mentioned that 3 more times it had done after it had changed with 8 ltr of water.
So the n will b 4.
Mind the tricks of the questions.
Do a very sharp calculation you will get it? It is much easier than its look.
The question is - "How much wine did the cask hold originally?".
So the method is :
(liquid A left after n'th operation) / (liquid B left after n'th operation) =[ (1- (b/a))^n]/[1- (1- (b/a) ^n].
Here, a= total amount of vessel(a.k.a wine);
b = amount of other liquid poured(a.k.a. water);
n = no of operations had done.
In this question they also mentioned that 3 more times it had done after it had changed with 8 ltr of water.
So the n will b 4.
Mind the tricks of the questions.
Do a very sharp calculation you will get it? It is much easier than its look.
Rahul.. said:
10 years ago
Given ratio i.e. 16/65 is wine/water.
Hence wine/(wine+water) is 16/81.
Total quantity of wine+water will remain fixed i.e. equal to initial quantity of wine i.e. x.
Hence final ratio of wine/(wine+water) will be (wine left/initial wine).
Hence it will be x (1-8/x)^n/x equal to 16/81.
Hence wine/(wine+water) is 16/81.
Total quantity of wine+water will remain fixed i.e. equal to initial quantity of wine i.e. x.
Hence final ratio of wine/(wine+water) will be (wine left/initial wine).
Hence it will be x (1-8/x)^n/x equal to 16/81.
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.
Ananta chatterjee said:
10 years ago
See the formula is well understood a(1-b/a)^n. Now even after adding and removing water we have the total amount o be the same that is x.
So we have 16/81 of x = This is the part of wine left that should be equal to the formula.
So we have 16/81 of x = This is the part of wine left that should be equal to the formula.
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