Aptitude - Ratio and Proportion - Discussion

Given:

- Total volume of the mixture = 60 liters.
- Ratio of milk to water = 2 : 1.

First, calculate the quantities of milk and water in the original mixture.
Let the quantity of milk be 2x and the quantity of water be x .
Since the total volume is 60 liters, we have:
2x + x = 60,
3x = 60,
x = 20.
So, the quantity of milk is 2x = 2 * 20 = 40 liters,
and the quantity of water is x = 20 liters.

Next, we need to determine how much water needs to be added to change the ratio of milk to water from 2:1 to 1:2.
Let y be the amount of water to be added.

The new quantity of water will be:
20 + y.

The new ratio of milk to water should be 1:2, which means:
40/{20 + y} = 1/2.

Now, solve for y :
40 = (1/2) (20 + y)
40 = {20 + y}/2,
80 = 20 + y,
y = 80 - 20,
y = 60.
Therefore, the quantity of water that needs to be added is: 60 liters

Total mixture is 60ltr which contains milk and water in the ratio 2:1, which means mixture contains 2 parts of milk and 1 part water.

2 parts + 1 part = 3 parts = 60 ltr.

Therefore 1 part =60/3 = 20 ltr.

Milk = 2 parts= 2* 20 =40 LTR.

Water = 1 part=1 * 20 = 20 ltr.

Now quantity of milk and water is changed in such a way to get the new amount of milk and water in the mixture as 1:2.

Now the 1 in 1:2 represent that the amount of milk in the mixture is not changed and it is same as 40ltr. The change is in the amount of water.

Here 1 part in 1:2 represent 40 ltrs of milk. Therefore 2 part 80 ltrs. That is we need 80 ltrs of water to get the new mixture ratio. We have 20 lts of water. Now additional 60 ltrs must be added.

So 60 ltrs is the answer.

Initial mix i.e, 60Ltr Old ration m : w :: 2 : 1 total parts 2 + 1 = 3parts of 60Ltr = 20Ltr.

Hence milk = 2 * 20 = 40Ltr, & water = 1 * 20 = 20Ltr.

But question is how much further or additional water is added to maintain the New Ratio 1 : 2 i.e, m : w :: 1 : 2 one should get Confused with initial mix i.e, 60Ltr.

Method of Substitution :
Already milk 40Ltr and water 20Ltr question is how much further or additional water is added to maintain the New Ratio 1 : 2.
We have [A]. 20 litres [B].30 litres [C].40 litres [D].60 litres.

Water should be 20 + either A,B,C,D but New Ratio 1 : 2 therefore w = 20 + 60 = 80 hence m:w = 40/80 = 1:2.

I hope you have understood the solution.

Initial ratio of milk : water = 2:1.
So (2+1=3) these 3 unit belongs to 60 litres.
Therefore, 2 units of milk belong to 40 litres and 1 unit of water belongs to 20 litres.

Further water is added so the ratio of milk: water = 1:2 => given.
As water is added but the previous quantity of milk is the same which is 40 litres(only ratio change).
So here we consider the 1 unit of milk as 40 litres and therefore 2 units of water is 80 litres.
The final quantity of water -Initial quantity of water = 80 - 20 = 60 litres.
Further water added is 60 litres.

Take 3 empty glass.

We have to count 60 ltr with the ratio,
Now fill 2 glass with milk 20ltr = 40ltr.
And,

Now fill 1 glass with water 20ltr,
Mix milk 2(glass) + water 1(glass) = 3glass.
The mixture is now of 20(milk)+20(milk)+20(water) = 60ltr.

Now we want a new ratio 1:2.
For that how much water to be added in existing 60ltr solution.

We have 40ltr of milk in 60ltr and 20ltr water.
If we added 60ltr of water now then milk is 40ltr and water is (20+60) 80 which is 1:2.

It is said in the question that the ratio is 2:1 which means 40 litres of milk and 20litres of water should be there. Now the new ratio should be 1:2 of the obtained result (40 litres stands for 1parts and 20 litres stands for 2 parts) now in this mixture there is 40 litres of milk and 80 litres of water. But there is already 20 litres of water is there in the previous 40 litre of milk so we deduct that 20 litres therefore we get new amount of water i.e. is 60 litres.

@Bagavathi.

In 60lts of mixture the ratio of milk and water is 2:1. It means 40lts of milk and 20 lts of water. In the question he just asked only how much of water is added to make the ratio of milk dan water to 1:2.

So the quantity of milk is unchanged i.e, 40lts. and the quantity of water required is 60lts. Now the total quantity of mixture is 120 lts in which 40lts of milk is 1part. In the old ratio the total mixture is 60lts so 40 lts of milk is 2part.

Total mixture is 60 litres.

1st ratio is 2:1 and the 2nd is 1:2.

So, 1st ratio for milk would be 60x2/3 = 40.

And water is 20(60-40).

2nd ratio is 1:2.

So milk should be 60x1/3 = 20.

And water is 40 according to the ratio.

And we already have 20 litres according to the first ratio. So we only have to 20 more litres to the earlier one and we get a total of 40 (20+20).

So the answer should have been 20 instead of 60. If wrong please correct me.

We have 60 litres of mixture.
Milk & water in the ratio 2:1 that means milk is 2 parts and water is 1
part. Totally mixture contains 3 parts(2+1=3 parts = 60 litres mixture).If we want to know the milk quantity thenwe have the general formula is Total mixture X (milk parts/total parts).

Milk quantity=milk parts/total parts
here milk parts=2
here total parts=milk parts+ water parts=2+1=3

Then milk quantity=2/(2+1);
=2/(3)
=2/3.

The ratio of milk to water is given as: 2:1.
Let us assume a quantity of milk is 2x ans water is x.
Therefore ,
2x + x = 60 liters (Total mixture).
3x = 60
x = 20 --------(1)

Now milk is 2x therefore 2*20 = 40 liters is milk.
Now new water is added therefore x becomes (20 + x),
now new ration is given 40 /(20+x) = 1/2,
80 = 20 + x.
x = 60 Liters.