Aptitude - Alligation or Mixture - Discussion

Discussion :: Alligation or Mixture - General Questions (Q.No.3)

3. 

A can contains a mixture of two liquids A and B is the ratio 7 : 5. When 9 litres of mixture are drawn off and the can is filled with B, the ratio of A and B becomes 7 : 9. How many litres of liquid A was contained by the can initially?

[A]. 10
[B]. 20
[C]. 21
[D]. 25

Answer: Option C

Explanation:

Suppose the can initially contains 7x and 5x of mixtures A and B respectively.

Quantity of A in mixture left = 7x - 7 x 9 litres = 7x - 21  litres.
12 4

Quantity of B in mixture left = 5x - 5 x 9 litres = 5x - 15  litres.
12 4

7x - 21
4
= 7
5x - 15  + 9
4
9

28x - 21 = 7
20x + 21 9

252x - 189 = 140x + 147

112x = 336

x = 3.

So, the can contained 21 litres of A.


Teja said: (Jan 8, 2011)  
Can You explain in other way ?

Amara said: (May 25, 2011)  
How to calculate mixture left?

Debjyoti said: (May 28, 2011)  
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)+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 u calculate further u ll get the X value as 36

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

Sree said: (Jun 12, 2011)  
Hi Debjyoti,

Can you give the explination how you got x=36 using below equation?

7(x-9)/12:(5(x-9)+9) = 7:9

Karthikeyini said: (Jun 26, 2011)  
(7x-(21/4))/((5x-(15/4))+9)

In this term how 9 occured at the end ? Can anyone explain this ?

Prithvi Chauhan said: (Jun 26, 2011)  
Please can you explain in any other simple way?

Gowtham said: (Sep 3, 2011)  
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

San said: (Sep 19, 2011)  
Is there any easy way to do it ?

Preethi said: (Sep 21, 2011)  
Any simple method please.

Silu said: (Oct 15, 2011)  
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...)

Varsha said: (Jan 18, 2012)  
Thanks silu.

Naveen said: (Jun 25, 2012)  
How should I know in this case I should take one variable.

Shravan said: (Aug 21, 2012)  
@Silu good explaintion.

Sus said: (Aug 31, 2012)  
@Silu your explanation is good.

Amisha said: (Sep 1, 2012)  
Suppose intial quantity of mixture is x
withdraw 9 lit so,qut. remain is x-9
(it can't change ratio A:B=7:5)
so, B is 5/12
alligation
5/12 1 9/16-5/12=7/48
1 - 9/16= 7/16
9/16(A:B=7:9 so, B=9/16)
7/16 7/48

qt of mixture (after withdraw of 9 lit)= 9lit
qt of pure liquid B=9 lit.
so, x-9/9= (7/16)/(7/48)
x-9/9 = 3
x-9 = 27
x = 27 + 9
x = 36
intial qt of mixture is 36 lit (contain A:B = 7:5)
so, qt of A = 7*36/12 = 21 lit

Karthik Rs said: (Sep 8, 2012)  
The Value of A is 7*x ... the only answer which is divisible by 7 is 21 .. so there you go :)

Amisha Patel said: (Sep 18, 2012)  
Suppose intial qt. of mixture is 9
withdraw 9 lit. so qt. remaining is x-9,but it can't change ratio so A:B = 7:5 and B = 5/12
apply alligation where,
c = 5/12
d = 1 (pure B is added)
mean = 9/16 (we want to make A:B= 7:9,so B= 9/16)
qt of mixture/qt of pure liquid B= (1-mean)/(mean-c)
x-9/9 = (1-9/16)/(9/16-5/12)
x-9/9 = (7/16)/ (7/48)
x-9/9 = 48/16
x-9/9 = 3
x-9 = 27
x = 27 + 9
x = 36
initial qt of mixture is 36 lit (contain A:B = 7:5)
so, qt of A = 7*36/(7+5) = 21 lit

Anil Kumar Jat said: (Dec 18, 2012)  
A B
7 : 5
7 : 9

9-5=4unit=9

1unit=9/4
16unit=36

A=36*7/12=21.
B=36*5/12=15.

Srividhya said: (May 3, 2013)  
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.

Unknown said: (Dec 4, 2013)  
Can't we find it by forming two linear equations?

Meeran said: (Dec 24, 2013)  
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.

Trilok said: (Dec 29, 2013)  
We need to find how many liters of liquid A present in the can initially. So it is given that ratio is 7:5. So clearly it is a multiple of 7. And, by looking at the options we get the answer as 21.

Vaishali said: (Apr 11, 2014)  
7:5.
7:9.

7+5 = 12.
9-5 = 4.

9/12*4 = 3.
3*7 = 21.

Rushita said: (Apr 28, 2014)  
How is it possible? please give me some explanation.

Nitish said: (Aug 2, 2014)  
Using allegation method.

At first ratio of 5/12, only B was filled by replacing 9l of mixture. So 9l of B was filled extra to fulfill the can.

1-9/16
--------- = 3:1.
9/16-5/12

Let capacity be x,
1/4*x = 9.
x = 36.

So, B = 15 and A = 21.

Akash said: (Feb 7, 2015)  
So easy. The answer should be a multiple of 7 as the initial ratio of A:B is 7:5.

And only 21 is in the option which is a multiple of 7. So option C.

Sneha said: (Mar 17, 2015)  
Why I take 12?

Karthika said: (Apr 29, 2015)  
We need to subtract 9 liters from mixture only. But why subtract from 2 liquids?

Karthika said: (Apr 30, 2015)  
Why 7(x-9) and 5(x-9)? Please help me.

Ankita said: (May 2, 2015)  
In the very first explanation how does 20x+21 come into picture? I mean just the 21.

Ricky said: (Jul 17, 2015)  
Even after drawing off some mixture, the mixture remains in the same ratio which is 7:5.

Now it 7x/(5x+9) =7/9 i.e. x=9/4.

Quantity of liquid A in the remaining mixture = 7X9/4 = 63/4.

And quantity of A in the drawn off mixture = (9/12)X7 = 63/12.

Total quantity is (63/4)+63/12 = 21 answer :).

Jumcy said: (Jul 30, 2015)  
See the ratio of A = 7, check the options which are divisible by 7, 21 is there, simple tricky way.

Sumanth said: (Aug 19, 2015)  
Most easy answer.

Check options for given ratio of 7:5. Only option is 21.

Check it if a is 21 then b=15.

a:b = 21:15.

Now take 9 liters from 21 i.e. 21-9=12 now add it to 15 becomes 27.

But after taking also ratio is 7:9. So answer is 21.

Renu said: (Sep 3, 2015)  
Hi Vaishali can you please explain.

Dipika said: (Sep 29, 2015)  
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.

Priya said: (Oct 1, 2015)  
I don't understand can you people explain me much better?

Priya said: (Oct 1, 2015)  
I don't understand can you people explain me much better?

Siddhesh said: (Nov 4, 2015)  
Can any one tell me how we calculate (5x-15/4)+9?

Ramakrishana said: (Dec 1, 2015)  
Just divide the 9 liters 7:5.

That is 21/4 and 15/4. They are 7x, 5x.

Then subtracted from their ratios.

That is 7x-21/4, 15x-15/4 then B is added to the mixture.

That is 15x-15/4+9.

((7x-21/4)):(5x-15/4+9) = 7:9.

You will get x = 3 then 7x = 21.

Ramakrishna said: (Dec 2, 2015)  
= (5x*4-15+9*4)/4.

Deepthi said: (Dec 28, 2015)  
Can any one explain it again please?

Kiran said: (Mar 9, 2016)  
Hi.

Can you explain me why we take 7/12 and 5/12?

Suraj said: (May 30, 2016)  
Here is the simplest method I'm going to discuss.

Since we are not adding anything in A.

Therefore.

After mixing A =7/(7 + 9) = 7/16.

7/16 = 7/12 (volume before replacement/volume after replacement).

7/16 = 7/12 ((12x - 9)/(12x - 9 + 9)).

Then, x = 6.

Then finally we get 21L.

Bony said: (Jun 15, 2016)  
We have two ratios 7:5 and 7:9, let's make it to 28:20 and 21:27 took LCM of their sum to make the total equal).

On drawing 9 litres, 7/12 * 9 = 21/4 amount of A is lost.
This 21/4 corresponds to a change of 7 units in the ratio (28 : 27, 28 : 20).

So 1 unit in the ratio corresponds to 21/(4 * 7) = 3/4.
Initial amount of A corresponds to 28 units (28:20) is our ratio, so 28 units = 28 * 3/4 = 21 litres.

No difficult equations involved. Just make sure that the sum of the ratios in initial and final cases remain the same.

Priyanka Kumari said: (Jul 19, 2016)  
Please, can anyone explain it in short term?

Simhachalam said: (Jul 22, 2016)  
@Anil Kumar Jat.

Your method is the easiest way to solve the problem. Thank you very much.

Rahul said: (Aug 5, 2016)  
Can we solve this problem with the formula of adulteration?

Prabhas said: (Aug 10, 2016)  
Assume 7 : 5 as 12 liters.

9 liters are drawn form the mixture.

So,

12 - 9 = 3.

Then,
7 * 3 = 21 and 5 * 3 = 15.

Sonu said: (Aug 13, 2016)  
@ Prabhas,

Your explanation is very nice and it also very useful.

Vini said: (Aug 15, 2016)  
If 1/4th of the total is 9.

That is, 1/4 * x = 9,

Then, total (x) = 36,

Therefore, 7/12 * 36 = 21.

Keerthana said: (Aug 23, 2016)  
9 x 7 = 63 how you got 81@Silu.

Gopika S S said: (Sep 27, 2016)  
Thanks @Srividhya, your explanation is much better.

Prakash said: (Nov 2, 2016)  
Hi, guys can anyone explain me from where 7x - 7/12 x 9 this fraction come?

Bharti said: (Nov 7, 2016)  
I like the your answer @Vini.

Vijay Padala said: (Nov 21, 2016)  
Good explanation, thanks to all.

Shiv Raj said: (Nov 26, 2016)  
Thanks for your explanation @Prabhas.

Gurpreet said: (Dec 2, 2016)  
@ Prabhas, how is this possible?

Ager mixture which is replaced more than the addition of ration like 7 + 5 = 12 as mixture value which is replaced is 18 litre then?

Hemanta said: (Dec 6, 2016)  
Thank Prabhas.

Sudhanshu said: (Dec 19, 2016)  
Initial7 : 5
Final 7 : 9

Change is of mixture B by 4 unit I.e of 9 litre.
So, 1 unit = 9/4,
16 unit =16 * (9/4) = 36 change is happening in final value of 9 + 7 = 16,
Initial A = 7 * 36/12 = 21 (7+5=12).

So A =21, B = 15.

Arjun said: (Jan 20, 2017)  
The formula is x*(1 - y/x )^n.
So 12 * (1 - 9/12)^1,
So the answer is 3.
Since we take 7x of A.
The answer is 7 * 3 = 21.

Teju said: (Feb 11, 2017)  
7x+5x-9 = 9x(mixture removed equals B added)
X = 3
7x = 21= A.

Eswararao S said: (May 8, 2017)  
When mixture removed, same 7:9 remains.

7 : 5 when Mixture B,
Gained 3 points of B mixture for 9 litres.
So 1 Point of mixture is 3 litres,
And, 7 Points of A mixture is 7 * 3= 21 litres.

Saurabh Mishra said: (May 11, 2017)  
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 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-
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.

Karen said: (May 14, 2017)  
Do we use the ratio? Please tell.

Kia said: (May 14, 2017)  
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.

Bdshahjahan said: (May 30, 2017)  
Good job @Silu, @Anilkumar.

Dhivya said: (Jun 30, 2017)  
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.

Dhivya said: (Jun 30, 2017)  
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.

Suri said: (Jul 3, 2017)  
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.

Sam said: (Jul 6, 2017)  
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.

Nihar said: (Jul 30, 2017)  
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.

Shashank Yadav said: (Jul 31, 2017)  
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.

Juli Burnwal said: (Sep 13, 2017)  
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.

Arjun Mahatma said: (Sep 30, 2017)  
Thanks @Anil Kumar Jat.

Kashif said: (Oct 30, 2017)  
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>.

Prashant Pal said: (Dec 6, 2017)  
@ALL.

7:5
7:9

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

Sai Sekhar said: (Feb 18, 2018)  
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.

Confused.Soul said: (May 20, 2018)  
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.

Confused.Soul said: (May 26, 2018)  
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.

Ankit Tiwari said: (Jul 21, 2018)  
@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.

Lakshminarasimha said: (Jul 26, 2018)  
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.

Aksh said: (Sep 8, 2018)  
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.

Ibu said: (Sep 24, 2018)  
Thanks @Debjyoti.

Aarav said: (Nov 26, 2018)  
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.

Shreya said: (May 11, 2019)  
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.

Anupom said: (May 30, 2019)  
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.

Rachana said: (Jul 13, 2019)  
@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!

Karandeep Singh said: (Jul 17, 2019)  
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.

Meghna said: (Jul 23, 2019)  
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.

Hossain said: (Jul 24, 2019)  
How 9 is added with B? Please explain.

Veeresh Nj said: (Sep 24, 2019)  
7:5 = 7 * 5 = 35.
7:9 = 7 * 9 = 63.

Now subtract both values;

63 - 35 = 28.
Now u see common value in 7:5 and 7:9.
Here 7 is common to subtract this value with 28.
A = 28 - 7 = 21.
A = 21.

Ankush Singh said: (Oct 3, 2019)  
7:5.
7:9.
Increase is part b 4.
4=9.
1=9/4.
2nd of total mix=16.
16= 9/4*16=36.
1st mix A is. 7/12*36 =21.

Haider said: (Dec 14, 2019)  
9 litres of the withdrawn mixture will also contain A:B = 7:5.
So (7+5)n = 12*n.
12*n = 9(given)
n=3/4.

So the quantity of A in withdrawn mixture = 7*3/4=21/4 litres.
So in original mixtures A will be remained = 7*x-21/4.

Which will be equal to the quantity of A in 2nd mixture.

So (7*x-21/4)=7*y................equation 1.

Also, sum of A & B in both the mixtures will be same,
(7+5)*x=(7+9)*y....................equation 2.

Solving both we will get x=3.
So the quantity of A =7*3=21 litres.

Yamini@Usha said: (Jan 31, 2020)  
It's very difficult to understand. Anyone please help me to get it.

Kalai said: (Feb 21, 2020)  
@Yamini.

Just simple initially there is 7:5 ratio of A & B now they need initial liters of A so in the answer which is a multiple of 7 is 21.

Simple one.

Tejashwini said: (Aug 15, 2020)  
@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.

Supriya Balaji said: (May 26, 2021)  
We can also solve if easily by using a formula, final QT/initial QT=(1-(x/c) ^t.
Where, initial QT = quantity.
x=how much QT is removed,
C=total capacity,
T=how many times the process is repeated, that is one time as per the quetion,

Final Qt = 12(1-(9/12)) ^1,
=12(12-9/12),
=3.

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