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.
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)
Shiv said:
4 years ago
Only wine 8 liters
and 3 times operation.
So, 8 * 3=24.
and 3 times operation.
So, 8 * 3=24.
(17)
Salaj Mondal said:
4 years ago
x^4 = 81
=>x=3
y^4=16
=>y=2
x - y
= 3 - 2
= 1.
1 ratio means 8 litre.
so, 3 ratio means 24 litre.
=>x=3
y^4=16
=>y=2
x - y
= 3 - 2
= 1.
1 ratio means 8 litre.
so, 3 ratio means 24 litre.
(3)
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)
Athira said:
3 years ago
Here, x is just used for simplification.
Suppose we write the equation as:
[x({1-(8/x)}^4)]/32 = 16/65 it is correct.
But, it will be very difficult to simplify because of the fifth power in the resulting equation that we have to solve.
So instead, we take the ratio of wine to total liquid in the end. We can find the total liquid by simply adding 16+65, ie, wine=water, so this is not an issue. This way, we can eliminate the x outside bracket in the numerator and find the answer very quickly.
Hope it's clear.
Suppose we write the equation as:
[x({1-(8/x)}^4)]/32 = 16/65 it is correct.
But, it will be very difficult to simplify because of the fifth power in the resulting equation that we have to solve.
So instead, we take the ratio of wine to total liquid in the end. We can find the total liquid by simply adding 16+65, ie, wine=water, so this is not an issue. This way, we can eliminate the x outside bracket in the numerator and find the answer very quickly.
Hope it's clear.
(1)
CHETHAN K P said:
3 years ago
Wine:water = 16 : 65
Total =16 + 65 = 81.
Now wine: total = 16:81.
Total =16 + 65 = 81.
Now wine: total = 16:81.
(16)
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