Aptitude - Ratio and Proportion - Discussion

Thank you karthik negi for your clear and crisp explanation.

@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.

The original ratio is 2:1.

That means 40 liters milk and 20 liters water.

We have to add x liters of water so that ratio becomes 1:2.

Here milk quantity doesn't change.

So in 1:2 ratio.

1 part is equal to 40liters.

2 parts-------------------?

80liters.

So the quantity of water to be added is 80-20=60.

Ramesh Nicely explained .....

Total Mixture 60 liter and ration of the milk and water is 2:1.
Then milk is 40 lit and water is 20 lit.

If you go options 40 has to be correct ?
40 : 20 => 40: 20+60 => 40: 80 => 1:2.

How can we assume that the second ratio (1:2) given in the problem for next 60 liters ?

Take it a simple way:

60 litre mixture
2:1 is the ratio means
Mixture is divided into 2+1 = 3 parts i.e, 30lt *3 = 60lt

Given 2:1 = milk: water = 40: 20
Now to make it 1:2
When 40:80=1:2
So, 80-20=60 lt water is added to bring out the ratio.

Old ratio is 2:1.
New ratio is 1:2.

So new ratio is multiply by 2 we get 2:4 (because we want water only).

Old ratio: 2:1.
New ratio: 2:4.

-----
0:3
-----

So (3/sum of old ratio) *60=3/3*60=60 is the answer. This method can be applied to all problems like this.

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.

Total mixture x=60 ltrs.

a:b=2:1(old ratio) c:d=1:2(new ratio).

x(ad-bc)/c(a+b).

= 60(2*2-1*1)/1(2+1).
= 60(4-1)/3.
= 60*3/3.
= 60 ltrs.