Aptitude - Alligation or Mixture - Discussion

How 9 is added with B? Please explain.

The 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 the 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---> If you calculate it, you will get the X value as 36.

Put that x value in A=7x/12, so here you can get answer of A contain initially.
A = 21.

A:B
7:5.

58% : 42%.

When 9 litres is drawn out from the mixture it will be drawn in the same proportion of their ratios.

9 litres( 5.22 litres of A and 3.78 litres of B)

Now 3.78 litres of B is replaced with 9 litres of B. So now ratios becomes A:B( 7:9 ie 43.75%:56%)

So, the difference of the solution B added( 9 litres - 3.78 litres = 5.22 litres )
now my unitary method if 5.22 litres is 56%-42% = 14%.
Total X litres 100%.

X total vessel qty = 37.2 litres.
Solution A in the mixture initially = 58% * 37.
= 21litres Approx.

@Kiran.

Because we have total mixture initially as 7+5=12.
And now as the ratio is 7:5.
i.e.
7/12 and 5/12 respectively!

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.

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.

Initial ratio= 7:5, total volume initially becomes 12 ---> eq1.
Final ratio after removing =7:9, total volume becomes 16 ---> eq 2.
Now, make the volume quantities equall by multi. Eq1 with16 and eq2*12.
Intial become 112:80.
Final become 84:108 = 21:27.
Therefore, the quantity of A becomes 21 is the answer.

Thanks @Debjyoti.

It is said that the ratio initially is 7:5, so the quantity of first is a multiple of 7, so 21 is the answer.

The total 9 drawn off ans filled.7:5,
3/4 parts drawnoff and filled,

For every 1part is 3 total 12 parts i.e 12*3=36,
7*3=21,5*3=15.