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 8 of 10.
Surya said:
7 years ago
Let the quantity of the wine in the cask originally be x litres. 8 litres of wine is removed from it and replaced with water. This operation is done a total 4 times. After 4 operations,
Wine : Water = 16 : 65 or Wine : Total = 16 : 81.
[(x-8)/x]4 = 16/81
(x-8)/x = 2/3
3x - 24 = 2x
x = 24
The correct option is D.
Wine : Water = 16 : 65 or Wine : Total = 16 : 81.
[(x-8)/x]4 = 16/81
(x-8)/x = 2/3
3x - 24 = 2x
x = 24
The correct option is D.
(3)
Shamika said:
7 years ago
How come 81?
Naeem said:
7 years ago
How come 81 in the denominator?
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.
Moideen said:
7 years ago
Well explained, Thanks @ Jayaraj @Jyoti.
Venkat said:
6 years ago
@All.
16x/81 is the quantity of wine in the mixture is given so equate to x(1-8/x)^4. (x is fixed litres of mixture).
16x/81 is the quantity of wine in the mixture is given so equate to x(1-8/x)^4. (x is fixed litres of mixture).
Vishnu vardhan said:
6 years ago
Yes, Total wine left = (16/81) * (initial litres of wine).
Vivek kumar said:
6 years ago
From where 16:81 came, there is 16:65? can anyone explain.
Rachana said:
6 years ago
@Vivek Kumar.
We have a formula for this to be solved.
(Q/T) = (1- (R/T) )^n.
Where
Q = Quantity of any liquid,
T = Total quantity of soln,
n = no.of operations,
R = Replacing quantity.
We have a formula for this to be solved.
(Q/T) = (1- (R/T) )^n.
Where
Q = Quantity of any liquid,
T = Total quantity of soln,
n = no.of operations,
R = Replacing quantity.
Prashant Shrestha said:
6 years ago
How come x(1-8/x)^4 = [x(1-8/x)^4] /x?
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