Aptitude - Alligation or Mixture - Discussion

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.

Thanks @Anil Kumar Jat.

Totally wrong answers. Why because total qty of B solution after drawn off and portion of B added is this,

5/12*x - 9*5/12 + 4y < where why is total qty of B added after drawn off and 4=9-5>.

@ALL.

7:5
7:9

9-5= 4
7+5= 12
So,
4/12 * 9= 3
So 7*3= 21.

Given ratios A:B is 7:9 and asked the initial quantity for that we check the options which are the multiples of 7.

In this case, 21 is only multiple 7. So directly we can say 21 is the answer.

A:B = 7:5

Total = 12 units
When 9 litres of mixture is removed, ((7/12) * 9) litres of A is removed, and ((5/12) * 9) litres of B is removed
Then 9 litres of B is added so that new ratio is 7:9.
In new mixture, Total volume of A is 7x - ((7/12) * 9) = 7x - 21/4.
And total volume of B is 5x - ((5/12) * 9) + 9 = 5x - 3 3/4 + 9 = 5x + 21/4,
So, (7x - 21/4)/(5x + 21/4) = 7/9.

Solving for x:
x=3.
Original Volume of A = 7x = 21,
Answer is D.

The total mixer is x.

A=7x/12 B=5x/12

After drawn 9 lit of mixer.

As Now, the basic principle is that;

When you remove any amount of the mixture, it removes both the liquids in the same ratio as the mixture itself.

So by above ratio (7/12)*9 and (5/12)*9 are to be removed

7x/12-7*9/12 = 7(x-9)/12
5x/12-5*9/12 = 5(x-9)/12
A=7(x-9)/12 and B=5(x-9)/12

now drawn 9 lit filled with B.
so B now contains B=5(x-9)+9/12.
now the new ratio of mixer is A:B=7:9.
we know the new value of A and B...........put that in this equation

7(x-9)/12:(5(x-9)+9)=7:9 ------> if you calculate further you willl get the X value as 36.

Put that x value in A=7x/12, so here you can get answer of A contain initially.

@All.

Let old ratio is 7:9.

And new ratio be 7:5.

Now according to question the quantity of A in mixture remains the same and displayed by ratio 7.

And the quantity of only b changes became from 9 to 5. So the difference between B quantity is (9-5) = 4 unit.
If 4 unit=9 Litre which is replaced then;
One unit= 9/4.
As from above total mixture is 7:5 initially we get 12*9/4=21 so the anser will be 21.