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 1 of 10.
Sanjay said:
1 decade ago
Could anyone explain the method above?
I couldn't make out why x is divided when it should have been divided by the quantity of water.
I couldn't make out why x is divided when it should have been divided by the quantity of water.
Sourav said:
1 decade ago
How did quantity of water become x?
Priya said:
1 decade ago
@sanjay
Its a formula....
[a(1-X/a)n]
a=initial quantity, X=quantity taken out, n=raised power on small bracket(no. of action done)
Its a formula....
[a(1-X/a)n]
a=initial quantity, X=quantity taken out, n=raised power on small bracket(no. of action done)
Divya said:
1 decade ago
Thanks priya.
Mamta said:
1 decade ago
Hi priya, thanks 4 giving formula can you explain why it is divded by x, why not by quantity of water.
Mayank said:
1 decade ago
Please tell what is the mean of performs operations more then three times. And why multiply x.
Sudheer said:
1 decade ago
Its 3 more times not "more then three times" so we used mul.
Chitwanjit said:
1 decade ago
How come it get divided by x, While it should be quantity of water ? Alternate way can be dividing by x and putting in 16/97 instead of 16/81.
Bappa said:
1 decade ago
Lets wine x
after 1st time wine remain x-8
now ratio of wine:water x-8:8
so 2nd time wine removed=(x-8)*(8/x)
after 2nd time wine remain=(x-8)-(x-8)*(8/x)
=(x-8){1-8/x}
=x(1-8/x)(1-8/x)
=x(1-8/x)^2
.........
for n time removaline remain=x(1-8/x)^n.
after 1st time wine remain x-8
now ratio of wine:water x-8:8
so 2nd time wine removed=(x-8)*(8/x)
after 2nd time wine remain=(x-8)-(x-8)*(8/x)
=(x-8){1-8/x}
=x(1-8/x)(1-8/x)
=x(1-8/x)^2
.........
for n time removaline remain=x(1-8/x)^n.
Himanshu said:
1 decade ago
Well explained Bappa.
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