Aptitude - Alligation or Mixture - Discussion

Let A initially be 7x & B be 5x.

The amount of A in a mixture is 7x /12& the amount of B in a mixture is 5x/12.
Let the total amount of mixture be x.

Now, it is given that 9litre of the mixture is taken out from the mixture & it can fill up with an amount of B.

Now, amount of new mixture be-
The Amount of A is 7(x-9)/12.
The amount of Bis 5(x-9)/12+9.

Now, it is given that the resultant ratio is 7/9.
7(X-9)/12:5(x-9)/12+9 = 7/9.
Now, it can easily solve to get the value of x=36 which is put in 7x/12 then get the amount of A is 21.

Do we use the ratio? Please tell.

Good job @Silu, @Anilkumar.

Initial A:B 7:5 ->12Parts.

New ratio A:B 7:9.
In the new ratio only 4 parts is changed so, 4parts=9litre.
for 12 parts =27litre + 9Litre.
Initial Litre is 36.
for Initial liquid A :7/12 *36 = 21Litre.

Initial A:B 7:5 ->12Parts.

New ratio A:B 7:9.
In the new ratio only 4 parts is changed so, 4parts=9litre.
for 12 parts =27litre + 9Litre.
Initial Litre is 36.
for Initial liquid A :7/12 *36 = 21Litre.

The Whole Question is clear but Why we are Multiplying with 9 in ration (7/12) *9.

What does multiplying with 9 litres means?

Please answer thank you.

A : B.
7 : 5
7 : 9

Here A is not changed ,but B added 9 liters more,
B = 9 - 5 = 4 difference by adding 9 on [ 9+7=16].
9/4 * 16 = 36.
Total is 36.
A =36 * 7/12 = 21.

A:B=7:9.
So total=12 parts.
after removing 9 litres.
A:B=7:9,
so 4 parts of b = 9 litres(change in ratio of b).
1 part=9/4,

So for total of 12 parts = (9/4)*12=27.
remaining liquid = 27+9(from mixture).
=36.
So A quantity= (7/12)*36=21.

The simplest way to do this question:

A and B are in a ratio of 7:5, we can say that, A=7x. A should definitely be a multiple of 7 and hence 21 is the answer.

Here we can see that there is only change in the liquid B.

7/5 (initially) and 7/9 (after drawn off the mixture and adding B).

So change in B liquid=9-5=4.
Now this 4 is the extra B liquid 5.
4 part=9lt.

So 12part (7+5) =27.
Now agn add the liquid mixture 9lt which was drawn off i.e 27+9=36lt.
Total=36lt.
So now A=36*7/12=21ans.