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 10 of 10.
Yogi damle said:
1 decade ago
If the answer is 24 liters then we cannot take out 8 liters of wine 4 times.
Amit said:
1 decade ago
After the first step of adding 8 liters of water, the cask contains a mix of wine and water so the next time we take 8 liters out, it could have 75 % wine or 35 % wine or any other amount. So, how can we calculate the final proportion of wine?
Shanjev said:
1 decade ago
Why the quantity of wine left in cask after 4 op is DIVIDED BY X, can anyone explain me?
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.
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)}.
Dileep said:
1 decade ago
@Reeya.
I didn't get you. what you are saying.
From the given information we can write it as,
x(1-8/x)^4 = 16/81.
i.e x = 24.
I didn't get you. what you are saying.
From the given information we can write it as,
x(1-8/x)^4 = 16/81.
i.e x = 24.
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