Aptitude - Alligation or Mixture - Discussion
Discussion Forum : Alligation or Mixture - General Questions (Q.No. 1)
1.
A vessel is filled with liquid, 3 parts of which are water and 5 parts syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?
Answer: Option
Explanation:
Suppose the vessel initially contains 8 litres of liquid.
Let x litres of this liquid be replaced with water.
| Quantity of water in new mixture = |  |
3 - | 3x | + x |  |
litres |
| 8 |
| Quantity of syrup in new mixture = | |
5 - | 5x | |
litres |
| 8 |
 |
|
3 - | 3x | + x | |
= | |
5 - | 5x | |
| 8 | 8 |
5x + 24 = 40 - 5x
10x = 16
| x = |
8 | . |
| 5 |
| So, part of the mixture replaced = | |
8 | x | 1 | |
= | 1 | . |
| 5 | 8 | 5 |
Discussion:
201 comments Page 7 of 21.
Uttam said:
2 decades ago
Let X=volume of vessel
Y=volume of mix taken out.
Initially,
volume of water in vessel=3X/8
volume of syrup in vessel=5X/8
Y=volume of mix taken out=volume of water added.
Now,
drawn off mix may contain,
volume of water=3Y/8.
volume of syrup=5Y/8.
after mix drawn off,
volume of water in the vessel=(3X/8)-(3Y/8)=(3/8)(X-Y).
volume of syrup in the vessel=(5X/8)-(5Y/8)=(5/8)(X-Y).
After water added, volume of water in the vessel
=[(3X/8)-(3Y/8)]+Y
=[(3/8)(X-Y)]+Y.
hence from the Question,in the vessel, volume of water
=volume of syrup
[(3/8)(X-Y)]+Y=(5/8)(X-Y)
10Y=2X
Y=(1/5)*X
So volume of water should be added is (1/5)th of volume of vessel.
Y=volume of mix taken out.
Initially,
volume of water in vessel=3X/8
volume of syrup in vessel=5X/8
Y=volume of mix taken out=volume of water added.
Now,
drawn off mix may contain,
volume of water=3Y/8.
volume of syrup=5Y/8.
after mix drawn off,
volume of water in the vessel=(3X/8)-(3Y/8)=(3/8)(X-Y).
volume of syrup in the vessel=(5X/8)-(5Y/8)=(5/8)(X-Y).
After water added, volume of water in the vessel
=[(3X/8)-(3Y/8)]+Y
=[(3/8)(X-Y)]+Y.
hence from the Question,in the vessel, volume of water
=volume of syrup
[(3/8)(X-Y)]+Y=(5/8)(X-Y)
10Y=2X
Y=(1/5)*X
So volume of water should be added is (1/5)th of volume of vessel.
Megha said:
2 decades ago
Thanks it is really a good way to solve it.
Ravi said:
2 decades ago
Uttam and surender. Your answer is perfect. Kiran is wrong.
Ramakhanna said:
2 decades ago
Thanks ameer for your detailed explanation...
Manasa said:
2 decades ago
Uttam, surender and ameer has cleared out my confusion regarding this problem. Thanks a lot.
Chacha chodhary said:
2 decades ago
Here is simple approach
3/5-1/2=1:1
3/5-1/2=1:1
Surya said:
2 decades ago
Can you solve this problem with allegation formula ?
Supreeth said:
1 decade ago
Victor your way of doing this problem is less time consumable. Thank you.
Hari said:
1 decade ago
As kiran said about getting the percentage. How its possible, can you explain it clealy of getting 60%, 40 %.
Preethi said:
1 decade ago
Excellant victor.
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