Aptitude - Alligation or Mixture - Discussion
Discussion Forum : 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?
Answer: Option
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 |
 |
|
= | 7 | |||||
|
9 |
 |
28x - 21 | = | 7 |
| 20x + 21 | 9 |
252x - 189 = 140x + 147
112x = 336
x = 3.
So, the can contained 21 litres of A.
Discussion:
100 comments Page 3 of 10.
Juli burnwal said:
8 years ago
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 liquid5.
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.
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
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.
Aarav said:
7 years ago
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.
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.
(1)
Ricky said:
1 decade ago
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 :).
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 :).
Supriya Balaji said:
4 years ago
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.
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.
(12)
SURAJ said:
9 years ago
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.
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.
Ramakrishana said:
10 years ago
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.
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.
(1)
NITISH said:
1 decade ago
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.
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.
Sumanth said:
1 decade ago
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.
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.
Nihar said:
8 years ago
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.
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.
Sudhanshu said:
9 years ago
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.
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.
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