Aptitude - Alligation or Mixture - Discussion

Thanks dilip I understood the solution very well.

Suppose a container contains x of liquid from which y units are taken out and replaced by water.
After n operations, the quantity of pure liquid = x 1 - y n units.

@ Krishna.

Your logic is correct but if its options are changed logically then your logic gets fail.

Please give a more suitable and simple explanation.

M.V. Krisna gave an excellent logic.

The total quantity of milk is 40.

Case:1. 4 lit pure milk is taken out and 4 lit water is added.
Now we have a mixture of milk and water that contains
36 lit milk and 4 lit water.(milk:water=36:4=9:1 means
In 10 lit mixture there is 9 lit milk and 1 lit water)

Case:2. 4 lit mixture taken out (i.e. 36 lit mixture remains).

Our 40(or 10) lit mixture contains 4(or 1) lit water
and 36(or 9) lit milk.

so 4 lit mixture which is taken out, contains
4*4/40=0.40 lit water and
4*36/40=3.6 lit milk.

(i.e., 4 - 4*9/10 = 4 - 3.6 = 0.4 lit water and
4 - 4*1/10 = 3.6 lit milk taken out.)
so, remained 36 lit contains 36 - 3.6 = 32.40 lit milk
and 4 - 0.4 = 3.6 lit water.

Now 4 lit water is added.
so, water in 40 lit mixture after addition is
3.6 + 4 = 7.6 lit.

At the end of second case we get
milk : water = 32.40 : 7.60 = 8.10 : 1.90

Case:3. 4 lit mixture taken out (i.e. 36 lit mixture remained).

Our 40 lit mixture contains 7.60 lit water and 32.40
lit milk.
so 4 lit mixture contains 4*7.60/40=0.76 lit water and
4*32.40/40=3.240 lit milk.

(i.e., 4 - 4*8.1/10 = 4 - 3.24 = 0.76 lit water and
4 - 4*1.9/10 = 3.24 lit milk taken out.)
so, remained 36 lit mixture contains
32.40 - 3.24 = 29.16 lit milk and 7.60 - 0.76 = 6.84
lit water.


Now 4 lit water is added.
so, water in 40 lit mixture after addition is
6.84 + 4 = 10.84 lit.

At the end of third case we get
milk : water = 29.16 : 10.84

@Krisna

If in option there is 28.9 then what will you do?

Krishna. Your idea is good.

Krishna your logic is good.

Given amount of milk = 40 lit.

Amount of milk taken out = 4 lit.

Remaining milk = 36 lit.

Given it is replaced with water and process repeated for twice.

Let us consider it is not replaced with water and process repeated for twice.

Then amount of milk = 36-4-4 = 28 lit.

Now logic:.

Now let us consider it is replaced with water and process repeated for twice.

Because of mixing water and taking 4 lit out from mixture, the amount of milk should be grater than 28 lit.

Only option (d) is greater than 28 lit.

Dont mind this is too long but i have a procedure to explain

Consider 3 times added water as 3 cases

case 1:after removal of milk and addition of water
water,milk are 4,36 lit ratio is 1:9

case2:when 4 lit are removed in that mix water,milk are (1/10)*4,(9/10)*4 of that mix
so presently water=4-2/5=18/5,milk=36-18/5=162/5
after addition of water,milk is same quantity but water=(18/5)+4
=38/4

case3:now ratio of water,milk=38:162=19:81
after removal of water,water,milk are (19/100)*4,(81/100)*4
so 19/25, 81/25
now milk=(162/5)-(81/25)=729/25=29.16 lit
antha length vodu anna dilogue gurthostundi kada so its simple to remember formula its better if we have only 1 or 2 cases