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 4 of 10.
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.
Shovik said:
1 decade ago
The real problem is that some of the initial steps are missing out here.
Amt. of wine left is given by x(1-8/x)^4.
Amt. of water left is given by x- x(1-8/x)^4.
So x(1-8/x)^4/[x-x(1-8/x)^4] = 16:65.
=> x(1-8/x)^4/x = 16:81.
Amt. of wine left is given by x(1-8/x)^4.
Amt. of water left is given by x- x(1-8/x)^4.
So x(1-8/x)^4/[x-x(1-8/x)^4] = 16:65.
=> x(1-8/x)^4/x = 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.
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.
Richa said:
1 decade ago
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/x)^4 litres.
x(1 - (8/x))^4 = 16x/81
(1 -8/x)= 2/3
(x - 8)/x =2/3
3x - 24 = 2x
x = 24.
Then, quantity of wine left in cask after 4 operations = x(1 -8/x)^4 litres.
x(1 - (8/x))^4 = 16x/81
(1 -8/x)= 2/3
(x - 8)/x =2/3
3x - 24 = 2x
x = 24.
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.
Atchiya said:
1 decade ago
I think performs operation more than 3 times means it includes the first time which is in process + 3 more times. So 4 times.
Please can anyone explain hoe that X came else explain this in alternative easy method.
Please can anyone explain hoe that X came else explain this in alternative easy method.
Pr!!!!! said:
1 decade ago
The ratio of wine to that of water is given as 16:81.
The initial quantity of wine is not given and it is assumed as 'x'.
And so the ratio becomes 16x:81.
And hence for simplification 'x' came in denominator.
The initial quantity of wine is not given and it is assumed as 'x'.
And so the ratio becomes 16x:81.
And hence for simplification 'x' came in denominator.
Shaswat said:
1 decade ago
@Prateek.
Here it is given that '8 liters are drawn from a cask full of wine' not 'wine and water'
so you cannot subtract i.e.,
Amt. of water left is given by x- x(1-8/x)^4.
So how can you subtract ?
Here it is given that '8 liters are drawn from a cask full of wine' not 'wine and water'
so you cannot subtract i.e.,
Amt. of water left is given by x- x(1-8/x)^4.
So how can you subtract ?
Karthiga said:
1 decade ago
The numerator 16(assume 16 liters) represents the quantity of remaining wine.
The denominator (16+65=81)represents
{the quantity of remaining wine +quantity of water added=initial quantity of wine(x)}.
The denominator (16+65=81)represents
{the quantity of remaining wine +quantity of water added=initial quantity of wine(x)}.
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