Aptitude - Alligation or Mixture - Discussion

Simple solution for this;

Given: Vessel contains...water -- 3 parts. Syrup -- 5 parts.

Required: Both should be half-- half

Sol: take one part of syrup and add it to water i.e then both will have 4 parts.

So divide syrup into 5 parts.then one part is 1/5, that is the solution.

Assume 30L water.
50L syrup.
Remove 20L liquid.

Than water will be 20L and syrup is 40L.
Add this 20L to water than 40L and 40L.
20/100 = 1/5.

Let us say that the quantity in the vessel is 8x units. It has 3x water and 5x syrup.
Now, let's say we withdraw 8y units of the mixture are replace them with water. When we take out 8y units of the mixture, we are actually taking out 3y water and 5y syrup. We are adding pure water back into the vessel.

New quantity of syrup = 5x - 5y.
New quantity of water = 3x - 3y + 8y = 3x + 5y.
They are equal to each other.
=> 5x - 5y = 3x + 5y.
=> 2x = 10y,
=> y/x = 2/10 = 1/5,
=> 8y/8x = 1/5k.

So, 1/5th of the mixture should be taken out and replaced with water.

3 : 5 is given.
1:1 we need,
3 : 5
1*5 : 1* 5
Difference 3 to 5 = 2
Total now 5+ 5
Then 2/ 10 ans is 1/5.

To make the given 3:5 equal we can take out 1 from 5 and add to 3(4:4). Since 1 is taken out from syrup so, the answer will be 1/5.

The ratio of syrup and water is 3:5 after replacing it will half-half(equal) -> 1:1
Because we are adding only water so the ratio of syrup will be same then ratio 1:1 become
5:5 means 2 ratio water is adding, total ratio is 5 + 5=10.
So 2/10=1/5

@Kiran.

Nice explanation.

As there are 3 parts of water and 5 parts of syrup.
total upto 8 parts.In terms of percentage,syrup is 60% and water is 40%.So syrup content to be reduced to 10% and water content to be increased to 10%,total constitutes to 10%+10%=20%.
finally 20%=20/100=1/5

Thank you Surender and Utham...i hav tried to explain the answer in detail

Let the volume of vessel be x
quantity of water = 3/8 x
quantity of syrup = 5/8 x

Let the amount of mixture removed be y
The removed mixture contains 3/8 y of water and 5/8 y of syrup

So quantity of water left in the mixture=3/8[x-y]
quantity of syrup left in the mixture 5/8 [x-y]

According to the question,the amount of mixture removed is replaced later by water,so that the syrup an water would be exactly half each of the mixture...

so when more water is added to the existing water in the mixture..

3/8[x-y] + y = 5/8[x-y]
3x/8 - 3y/8 +y = 5x/8 - 5y/8
y = 2x/8 - 2y/8
8y=2[x-y]
4y=x-y
x=5y
y=1/5 x

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?