Aptitude - Alligation or Mixture - Discussion

9 litre of the mixture is drawn from the total mixture but id doesn't change the ratio.
So the ratio remains as same as before 7:5.
After removing the 9-litre mixture, let the amount of A = 7x and B=5x; Total 12x.
So before removing the total amount of mixture was= 12x+9.

According to question:

7x:(5x+9)=7:9.
7x/(5x+9)=7/9,
x/(5x+9)=1/9,
9x=5x+9,
4x=9.
x=9/4.
12x= (9*12)/4.
12x=27,
12x+9= 27+9,
12x+9=36.

So the total amount of A and B in mixture= 36 Ltr.

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.

Total mixer is x.
A=7x/12 B=5x/12
after drawn 9 lit of mixer........
mixer remain(x-9)

So the new ratio of A:B is ...
A=7(x-9)/12 and B=5(x-9)/12
now drawn 9 lit filled with B
so B now contain B=5(x-9)/12 +9...........
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)/12+9)=7:9
=>9x-81=5x-45+108
=>x=36

as knon A=7x/12

=>A=7*36/12
=21
(enjoy...)

Hi guys,

Find the pure liqued of A in initial

Assume pure liqued x,
Quantity of a measured left formula=(pure A liquid - mix liquid)
Pure liquid of A=7x
Mix liquid of A=(7/12)*9
here 9 is also mixture

So, quantity of a measured left A=(7x-(7/12)*9)=7x-21/4
the same rule
quantity of a measured left B=(5x-(5/12)*9)=5x-15/4
(7x-(21/4)/5x-(15/4)+9)=7/9

Given here that 9 is add with b
ans x=3
ratio of 7

So=7*3=21 that all

@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.

Fraction of B in original mixture = 5/12 [A:B = 7:5 so B = 5/12].

Fraction of B in resultant mixture = 9/16 [A:B = 7:9 so B = 9/16].

Fraction of B in second mixture = 1 [replacement is made by B so B is 100%].

Applying the rule of allegation.

9/16-5/12 = 7/48.

1-9/16 = 7/16.

Therefore, ratio is 3:1.

Hence amount of liquid transferred was [(3*9)+(1*9)] = 36.

So amount of A = 7/12*36 = 21.

Simple Method: Forget B.

Let the total mixture be x litres.
So A will be (7x/12) lts.

After removing 9 lts, (7x9)/12 litres of A is gone.

So A will become (7x/12)-((7x9)/12).
Which is 7x/16 litres of the new mixture.

=>(7x/12)-((7x9)/12) = 7x/16.
=> 7(x-9)/12 = 7x/16.
=> (x-9)/3 = x/4.
=> 4x-36 = 3x.
=> x = 36 litres.

A in the original mixture = (7x36)/12 = 21 litres.

Ratio was 7:5 initially and 7:9 after drawn 9 lit from A to B.

Hence, Watching only the ratio of A liquid before and after the change we get.

Before : (7/12) * (x-9) Since, said 9 lit drawn and added to B.

After : 7 Given in the question itself as 7:9 ratio.

Since given both are the ratio, equating the both above we get,

(7/12) * (x-9) = 7 => x-9 = 12 => x = 21 lit.

@All.

Simply, the solution is;
Initially, 7/12 amount of liquidA is present in the mixture.
Finally, 7/16 amount of liquidA is present in the mixture.

Let us assume there is x litres of mixture.
9litres of the mixture is drawn out of x litres.

Final proportion = initial proportion(after removing/final volume).
You will get x = 36.
Therefore 7/12(x) = 21.

A:B = 7:5.

In 9L from the mix,
A = (7*9)/12 =5.25
B = (5*9)/12=3.75

In 9 L, ratio of A:B=5.25 : 3.75
Now, 9L of mix is removed and 9L of B is added
A = 7k-5.25.
B=5k--3.75+9 (9 is added because 9L of B is added)

We have ratio,A : B = 7:9.
A/B=7/9 = (7K-5.25)/(5K+5.25).
7(5K+5.25) = 9(7K-5.25).

On solving we get, K=3.
A =7K.
A = 7 * 3 = 21L.

Answer is C.