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:
198 comments Page 15 of 20.
K.S PAL said:
1 decade ago
A container is filed with 3 part water & 5 parts syrup, so total we have 8 parts or mathematically we can say,
3/8 water.
5/8 syrup.
Suppose we withdraw x parts of mixture then this will contain,
3/8(x) water.
5/8(x) syrup.
Now we have to add same amount of water the amount of water and syrup will be equal, so mathematically.
3/8-3/8(x) +x = 5/8-5/8(x).
It will give x = 1/5.
3/8 water.
5/8 syrup.
Suppose we withdraw x parts of mixture then this will contain,
3/8(x) water.
5/8(x) syrup.
Now we have to add same amount of water the amount of water and syrup will be equal, so mathematically.
3/8-3/8(x) +x = 5/8-5/8(x).
It will give x = 1/5.
Usha said:
1 decade ago
How we get 5x+24=40-5x?
Rajesh said:
1 decade ago
Simple friends,
Here totally 8 parts (5 part syrup + 3 part water).
To make it equal (4 parts syrup + 4 part water).
So, we have to draw 1 part from syrup (i.e.,) 1/5.
Here totally 8 parts (5 part syrup + 3 part water).
To make it equal (4 parts syrup + 4 part water).
So, we have to draw 1 part from syrup (i.e.,) 1/5.
Rahul Wiley said:
1 decade ago
Hey Keep it simple.
Fraction of syrup in final Mixture = (Fraction of syrup in initial mixture)*(1 - x/v).
Where,
x is the Quantity of mixture removed.
V is the volume of the Mixture.
Fraction of syrup in final Mixture = (Fraction of syrup in initial mixture)*(1 - x/v).
Where,
x is the Quantity of mixture removed.
V is the volume of the Mixture.
Akshara said:
1 decade ago
How would you taken 1/8 as a part of mixture in the last step? could you please explain?
(1)
Viswavikram said:
1 decade ago
Can we able to solve this problem in alligation method, if so explain?
(1)
Abhidhamm said:
1 decade ago
Ratio given is 3:5 (AS 3 Part water & 5 part syrup).
Take even LCM of 3 & 5 i.e. 24, 30 etc.
Suppose we take 24 as LCM.
Now divide LCM by 8 (addition of ratios i.e. 3+5).
So, 24/8=3.
Now, multiply both the terms of ratio by 3.
So we get 9 (water) and 15 (syrup).
As we have to make equal ratio we have to transfer 3 to water from syrup i.e. 15. So that both becomes 12.
So we get 3/15= 1/5.
Take even LCM of 3 & 5 i.e. 24, 30 etc.
Suppose we take 24 as LCM.
Now divide LCM by 8 (addition of ratios i.e. 3+5).
So, 24/8=3.
Now, multiply both the terms of ratio by 3.
So we get 9 (water) and 15 (syrup).
As we have to make equal ratio we have to transfer 3 to water from syrup i.e. 15. So that both becomes 12.
So we get 3/15= 1/5.
(1)
Radheshyam said:
1 decade ago
Let volume is 8.
Water = 3/8 syrup = 5/8.
According to question,
Suppose y mixture(water,syrup)are drawn.
Water quantity is 3y/8 and syrup quantity is 5y/8.
3/8-3y/8+y = 5/8-5y/8.
y = 1/5.
Water = 3/8 syrup = 5/8.
According to question,
Suppose y mixture(water,syrup)are drawn.
Water quantity is 3y/8 and syrup quantity is 5y/8.
3/8-3y/8+y = 5/8-5y/8.
y = 1/5.
(1)
Tapan kumar raul said:
1 decade ago
It is a common sense.
Finally in the solution 50% syrup & 50% water will remain.
That means if the solution will (5+3) =8 liters after drawn the mixture syrup will remain 4 liters. That mean the amount of mixture drawn contains 1 liter syrup => 5x = 1 liter.
=> 8x = 8/5 = 1600ml which is 1/5 part of 8 liter.
Finally in the solution 50% syrup & 50% water will remain.
That means if the solution will (5+3) =8 liters after drawn the mixture syrup will remain 4 liters. That mean the amount of mixture drawn contains 1 liter syrup => 5x = 1 liter.
=> 8x = 8/5 = 1600ml which is 1/5 part of 8 liter.
(1)
Sybil said:
1 decade ago
A solution of sugar syrup has 15% sugar. Another solution has 5% sugar. How many litres of the second solution must be added to 20% litres of the first solution to make a solution of 10% sugar?
(1)
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