good one

[navingulia]

a full glass has 3 parts milk and 1 part water.
What fraction of the glass should be emptied and water added to make the solution 1/2 milk, 1/2 water.

[namrata]

1/3 fraction of the glass should be emptied

[navingulia]

bilkul sahi namrata ji.
but the difficult part is to explain to some one how you arrived at this answer.

[mbamal]

Well the explanation is straightforward,

originally let the glass have 3 parts of milk and 1 part of water...

3 + 1 = 4

let n be the factor by which solution is emptied...multiply both sides by (1-n)...which is remaing capacity of glass..since milk and water will also be decreased in same ratio assuming a homogenous mix of milk and water

3(1-n) + (1-n) = 4(1-n)

now let water be increased by a factor of p

new solution has

3(1-n) milk

and

(1-n)p water

now 3(1-n) = (1-n)p..since now water and milk are equal

p = 3

total quantity in glass

= 3(1-n) + (1-n)p =6(1-n) since p = 3

now 6(1-n) = 4(capacity of glass)

n = 1/3 this implies that 1/3 of glass has to be emptied...

and amount of water now is 2 and amount of milk is also 2

Regards,

Mandeep

[navingulia]

excellent work bamal ji but i will give you a short explaination which i figured out
suppose u know the fraction to be emptied and empty it. in the remaining glass there should be 1/2glass milk since u r not going to add milk, u r going to add only water.
Now if 1/2 glass is milk 1/3rd of 1/2 i.e 1/6 should be water.
total solution= 1/2milk+1/6water=2/3
i.e u have emptied 1/3rd