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.
Hardeep Singh said:
9 years ago
Let initial quantity of wine = x.
After, 4 operations, quantity of wine left = x(1 - 8/x)^4.
Also the quantity of wine in the jar = (16/81)x.
Therefore, x(1-8/x)^4 = (16/81)x.
On solving, x = 24.
After, 4 operations, quantity of wine left = x(1 - 8/x)^4.
Also the quantity of wine in the jar = (16/81)x.
Therefore, x(1-8/x)^4 = (16/81)x.
On solving, x = 24.
Ajai said:
4 years ago
@All
Here is the explanation for Why it was divided by x?
Here the answer,
16/81 is a wine part of total volume initial x.
So that's why :(16/81)(x) --->step 2
And x goes LHS to denominator x.
Here is the explanation for Why it was divided by x?
Here the answer,
16/81 is a wine part of total volume initial x.
So that's why :(16/81)(x) --->step 2
And x goes LHS to denominator x.
(5)
Kola.shiva said:
1 decade ago
Simple method.
8 liters of original wine drawn from the cask.
So question they had given at last the ratio is 16:65.
So we add recent 8 liters to present ratio of wine.
16+8 = 24. Simple.
8 liters of original wine drawn from the cask.
So question they had given at last the ratio is 16:65.
So we add recent 8 liters to present ratio of wine.
16+8 = 24. Simple.
(1)
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.
Prakash said:
7 years ago
Use the formula (x-8/x)n = 16 / 81.
where n is 4,
x is original liquid (x-8) is the original liquid remaining after the exchange that is 16,
x the original quantity will be 65+16=81.
where n is 4,
x is original liquid (x-8) is the original liquid remaining after the exchange that is 16,
x the original quantity will be 65+16=81.
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.
Salman said:
3 years ago
x(1 - (8/x))^4 = 16
-> x 81.
In this statement, where did the extra "x" in the denominator come from? Also when the ratio is 16:65, then how is it changed to 16:81?
-> x 81.
In this statement, where did the extra "x" in the denominator come from? Also when the ratio is 16:65, then how is it changed to 16:81?
(1)
Vivek Rajput said:
5 years ago
@Sanjay(first comment) x is the total quantity.
x(1 - (8/x))4
--------------- = 16/81.
x
the numerator is the quantity of wine left and the denominator is the total quantity.
x(1 - (8/x))4
--------------- = 16/81.
x
the numerator is the quantity of wine left and the denominator is the total quantity.
Sahil said:
1 decade ago
Equation should be equated with 16/97.
Sine wine to water ratio is 16:81.
So wine to total ratio is 16:97.
Thats what we finding out actually by dividing it by x.
Sine wine to water ratio is 16:81.
So wine to total ratio is 16:97.
Thats what we finding out actually by dividing it by x.
PUNITH MISHRA P said:
1 decade ago
It is like this:
x(1-(8/x)^4)-(1) gives quantity of wine, whereas final ratio is 16/81. So final wine quantity is (16/81)*x which is equal to (1).
x(1-(8/x)^4)-(1) gives quantity of wine, whereas final ratio is 16/81. So final wine quantity is (16/81)*x which is equal to (1).
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